The On-Line Encyclopedia of Integer Sequences (OEIS)

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A291758

Compound filter (prime signature of n & sum of squarefree divisors of n): a(n) = P(A046523(n), A048250(n)), where P(n,k) is sequence A000027 used as a pairing function.
(history; published version)

#7 by N. J. A. Sloane at Sun Sep 10 14:53:56 EDT 2017

STATUS

proposed

approved

#6 by Antti Karttunen at Sun Sep 10 12:25:26 EDT 2017

STATUS

editing

proposed

#5 by Antti Karttunen at Sun Sep 10 12:19:11 EDT 2017

LINKS

Antti Karttunen, <a href="/A291758/b291758.txt">Table of n, a(n) for n = 1..16385</a>

Discussion

Sun Sep 10

12:25

Antti Karttunen: ~360 chars in data-section because used for filtering.

#4 by Antti Karttunen at Sun Sep 10 12:13:22 EDT 2017

NAME

Compound filter (prime signature of n & sum of squarefree divisors of n): a(n) = P(A046523(n), A048250(n)), where P(n,k) is sequence A000027 used as a pairing function.

#3 by Antti Karttunen at Sun Sep 10 12:12:20 EDT 2017

PROG

A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));

#2 by Antti Karttunen at Sun Sep 10 12:11:27 EDT 2017

NAME

allocated for Antti KarttunenCompound filter: a(n) = P(A046523(n), A048250(n)), where P(n,k) is sequence A000027 used as a pairing function.

DATA

1, 8, 12, 19, 23, 142, 38, 53, 25, 259, 80, 265, 107, 412, 412, 169, 173, 265, 212, 418, 672, 826, 302, 619, 40, 1087, 63, 607, 467, 5080, 530, 593, 1384, 1717, 1384, 1117, 743, 2086, 1836, 844, 905, 7780, 992, 1093, 607, 2932, 1178, 1759, 59, 418, 2932, 1390, 1487, 619, 2932, 1105, 3576, 4471, 1832, 8575, 1955, 5056, 915, 2209, 3922, 14908, 2348, 2092, 5056

OFFSET

1,2

FORMULA

a(n) = (1/2)*(2 + ((A046523(n)+A048250(n))^2) - A046523(n) - 3*A048250(n)).

PROG

(PARI)

A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from Charles R Greathouse IV, Aug 17 2011

A291758(n) = (1/2)*(2 + ((A046523(n)+A048250(n))^2) - A046523(n) - 3*A048250(n));

CROSSREFS

Cf. A000027, A046523, A048250, A291750, A291752, A291757.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Sep 10 2017

STATUS

approved

editing

#1 by Antti Karttunen at Thu Aug 31 07:53:08 EDT 2017

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved