The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A356414 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A356414

Number k such that k and k+1 both have an equal sum of even and odd exponents in their prime factorization (A356413).
(history; published version)

#8 by Michael De Vlieger at Sun Aug 07 07:53:19 EDT 2022

STATUS

reviewed

approved

#7 by Michel Marcus at Sun Aug 07 03:50:47 EDT 2022

STATUS

proposed

reviewed

#6 by Amiram Eldar at Sun Aug 07 03:50:22 EDT 2022

STATUS

editing

proposed

#5 by Amiram Eldar at Sun Aug 07 03:49:54 EDT 2022

LINKS

Amiram Eldar, <a href="/A356414/b356414.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#4 by N. J. A. Sloane at Sat Aug 06 08:09:25 EDT 2022

STATUS

proposed

approved

#3 by Amiram Eldar at Sat Aug 06 03:48:09 EDT 2022

STATUS

editing

proposed

#2 by Amiram Eldar at Sat Aug 06 03:37:44 EDT 2022

NAME

allocated for Amiram EldarNumber k such that k and k+1 both have an equal sum of even and odd exponents in their prime factorization (A356413).

DATA

819, 1035, 1196, 1274, 1275, 1449, 1665, 1924, 1925, 1988, 2324, 2331, 2540, 3068, 3195, 3324, 3339, 3549, 3555, 3626, 3717, 4164, 4220, 4235, 4556, 4598, 4635, 4675, 4796, 5084, 5525, 5634, 5660, 6003, 6027, 6068, 6164, 6363, 6740, 6867, 6908, 7028, 7227, 7275

OFFSET

1,1

COMMENTS

Numbers k such that A350386(k) = A350387(k) and A350386(k+1) = A350387(k+1).

EXAMPLE

819 is a term since A350386(819) = A350387(819) = 2 and A350386(820) = A350387(820) = 2.

MATHEMATICA

f[p_, e_] := (-1)^e*e; q[1] = True; q[n_] := Plus @@ f @@@ FactorInteger[n] == 0; Select[Range[10^4], q[#] && q[# + 1] &]

PROG

(PARI) is(n) = {my(f = factor(n)); sum(i = 1, #f~, (-1)^f[i, 2]*f[i, 2]) == 0};

is1 = is(1); for(k = 2, 10^4, is2 = is(k); if(is1 && is2, print1(k-1, ", ")); is1 = is2);

CROSSREFS

Cf. A350386, A350387, A356413.

KEYWORD

allocated

nonn

AUTHOR

Amiram Eldar, Aug 06 2022

STATUS

approved

editing

#1 by Amiram Eldar at Sat Aug 06 03:33:58 EDT 2022

NAME

allocated for Amiram Eldar

KEYWORD

allocated

STATUS

approved