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Search: a104903 -id:a104903
Displaying 1-6 of 6 results found.
page 1
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A136540
Numbers n such that sigma(n) = 7*phi(n).
+10
7
12, 78, 140, 910, 2214, 4180, 4674, 8008, 16120, 25758, 27170, 46816, 54530, 58302, 94240, 99484, 116116, 200260, 233740, 257140, 264160, 350740, 371898, 383656, 479864, 518022, 523218, 551540, 561340, 575598, 616722, 646646, 785118, 965960, 1027000
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If 2^p-1 is a Mersenne prime greater than 3 then m = 65*2^(p-2)*(2^p-1) is in the sequence (the proof is easy).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)
Kevin A. Broughan and Daniel Delbourgo, On the Ratio of the Sum of Divisors and Euler’s Totient Function I, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8.
Kevin A. Broughan and Qizhi Zhou, On the Ratio of the Sum of Divisors and Euler's Totient Function II, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.
EXAMPLE
sigma(12) = 28 = 7*phi(12) so 12 is in the sequence.
MAPLE
with(numtheory): A136540:=n->`if`(sigma(n)=7*phi(n), n, NULL): seq(A136540(n), n=1..10^5); # Wesley Ivan Hurt, Feb 11 2017
MATHEMATICA
Do[If[DivisorSigma[1, n]==7*EulerPhi[n], Print[n]], {n, 600000}]
(* Second program *)
Select[Range[10^6], DivisorSigma[1, #] == 7 EulerPhi@ # &] (* Michael De Vlieger, Feb 12 2017 *)
PROG
(PARI) is(n)=sigma(n)==7*eulerphi(n) \\ Charles R Greathouse IV, May 09 2013
CROSSREFS
Cf. A000043, A000668, A068390, A104900, A104901, A104902, A104903.
KEYWORD
easy,nonn
AUTHOR
Farideh Firoozbakht, Jan 05 2008
STATUS
approved
A171256
Numbers n such that sigma(n) = 10*phi(n) (where sigma=A000203, phi=A000010).
+10
5
168, 270, 570, 2376, 2436, 5016, 6426, 7110, 13566, 15834, 34452, 58520, 62568, 72732, 75210, 113832, 126882, 168756, 169218, 191862, 199368, 223938, 240312, 280488, 308568, 321468, 420888, 449442, 472758, 661848, 673608, 776736, 848540, 854496, 907236
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If n is in this sequence, then for any prime p not dividing n, sigma(np) - 10*phi(np) = 2*sigma(n).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)
Kevin A. Broughan and Daniel Delbourgo, On the Ratio of the Sum of Divisors and Euler’s Totient Function I, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8.
Kevin A. Broughan and Qizhi Zhou, On the Ratio of the Sum of Divisors and Euler's Totient Function II, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.
MATHEMATICA
Select[Range[10^6], DivisorSigma[1, #] == 10 * EulerPhi[#] &] (* Amiram Eldar, Dec 04 2019 *)
PROG
(PARI) for(k=1, 10^6, sigma(k) - 10*eulerphi(k) || print1(k", "));
CROSSREFS
Cf. A062699, A068391, A074400, A068390, A136547, A104900, A136540, A104901, A163667, A171257, A104902, A171258, A171259, A171260, A104903.
KEYWORD
nonn
AUTHOR
M. F. Hasler, Mar 19 2010
STATUS
approved
A171257
Numbers n such that sigma(n) = 11*phi(n) (where sigma=A000203, phi=A000010).
+10
5
2580, 16770, 18630, 28896, 35970, 61404, 66024, 147576, 163944, 215124, 224010, 296184, 399126, 408672, 443394, 464340, 476010, 574308, 856086, 862752, 868428, 931224, 957348, 1004910, 1110186, 1496610, 1721720, 1723290, 1833348, 1971288, 2139852, 2234790
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)
Kevin A. Broughan and Daniel Delbourgo, On the Ratio of the Sum of Divisors and Euler’s Totient Function I, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8.
Kevin A. Broughan and Qizhi Zhou, On the Ratio of the Sum of Divisors and Euler's Totient Function II, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.
MATHEMATICA
Select[Range[10^6], DivisorSigma[1, #] == 11 * EulerPhi[#] &] (* Amiram Eldar, Dec 04 2019 *)
PROG
(PARI) for(k=1, 2e6, sigma(k) - 11*eulerphi(k) || print1(k", "));
CROSSREFS
Cf. A062699, A068391, A068390, A136547, A104900, A136540, A104901, A163667, A171256, A104902, A171258, A171259, A171260, A104903.
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht and M. F. Hasler, Mar 19 2010
STATUS
approved
A171258
Numbers n such that sigma(n) = 13*phi(n) (where sigma=A000203, phi=A000010).
+10
5
630, 5544, 11160, 18810, 27000, 57000, 80388, 161820, 178020, 182880, 242820, 265608, 388620, 391500, 447678, 465192, 522522, 671760, 690120, 711000, 775170, 826500, 901170, 1051830, 1102290, 1157130, 1418160, 1578330, 1679400, 1812384, 1874520, 1993824
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)
Kevin A. Broughan and Daniel Delbourgo, On the Ratio of the Sum of Divisors and Euler’s Totient Function I, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8.
Kevin A. Broughan and Qizhi Zhou, On the Ratio of the Sum of Divisors and Euler's Totient Function II, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.
MATHEMATICA
Select[Range[2*10^6], DivisorSigma[1, #]==13EulerPhi[#]&] (* Harvey P. Dale, Mar 29 2018 *)
PROG
(PARI) for(k=1, 2e6, sigma(k) - 13*eulerphi(k) || print1(k", "));
CROSSREFS
Cf. A062699, A068391, A068390, A136547, A104900, A136540, A104901, A163667, A171256, A171257, A104902, A171259, A171260, A104903.
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht and M. F. Hasler, Mar 19 2010
STATUS
approved
A171259
Numbers n such that sigma(n) = 14*phi(n) (where sigma=A000203, phi=A000010).
+10
5
420, 2730, 5940, 12540, 24024, 38610, 48360, 66528, 77490, 81510, 133920, 140448, 141372, 156420, 163590, 282720, 284580, 298452, 348348, 498420, 600780, 681912, 701220, 771420, 792480, 901530, 918918, 1016730, 1052220, 1150968, 1372680, 1439592, 1654620
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)
Kevin A. Broughan and Daniel Delbourgo, On the Ratio of the Sum of Divisors and Euler’s Totient Function I, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8.
Kevin A. Broughan and Qizhi Zhou, On the Ratio of the Sum of Divisors and Euler's Totient Function II, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.
MATHEMATICA
Select[Range[10^6], DivisorSigma[1, #] == 14 * EulerPhi[#] &] (* Amiram Eldar, Dec 04 2019 *)
PROG
(PARI) for(k=1, 2e6, sigma(k) - 14*eulerphi(k) || print1(k", "));
CROSSREFS
Cf. A062699, A068391, A068390, A136547, A104900, A136540, A104901, A163667, A171256, A171257, A104902, A171258, A171260, A104903.
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht and M. F. Hasler, Mar 19 2010
STATUS
approved
A171260
Numbers n such that sigma(n) = 15*phi(n) (where sigma=A000203, phi=A000010).
+10
5
840, 11880, 12180, 25080, 32130, 67830, 79170, 172260, 282744, 312840, 363660, 569160, 596904, 634410, 696696, 843780, 846090, 959310, 996840, 1119690, 1201560, 1402440, 1542840, 1607340, 1929312, 2104440, 2247210, 2363790, 3309240, 3368040, 3883680
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)
Kevin A. Broughan and Daniel Delbourgo, On the Ratio of the Sum of Divisors and Euler’s Totient Function I, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8.
Kevin A. Broughan and Qizhi Zhou, On the Ratio of the Sum of Divisors and Euler's Totient Function II, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.
MATHEMATICA
Select[Range[10^6], DivisorSigma[1, #] == 15 * EulerPhi[#] &] (* Amiram Eldar, Dec 04 2019 *)
PROG
(PARI) for(k=1, 3e6, sigma(k) - 15*eulerphi(k) || print1(k", "));
CROSSREFS
Cf. A062699, A068391, A068390, A136547, A104900, A136540, A104901, A163667, A171256, A171257, A104902, A171258, A171259, A104903.
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht and M. F. Hasler, Mar 19 2010
STATUS
approved
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