A069164 Numbers k such that k*Sum_{d|k} 1/tau(d) is an integer.

1, 2, 12, 20, 24, 28, 36, 40, 44, 52, 56, 68, 72, 76, 80, 88, 92, 104, 116, 124, 136, 148, 152, 160, 164, 172, 184, 188, 212, 232, 236, 240, 244, 248, 268, 284, 292, 296, 316, 328, 332, 344, 356, 376, 388, 404, 412, 424, 428, 432, 436, 452, 472, 480, 488, 508

Offset: 1

Author

Benoit Cloitre, Apr 09 2002

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Vaclav Kotesovec, Plot of a(n)/(n*log(n)) for n = 2..100000

Crossrefs

Cf. A000005.

Programs

Mathematica

Select[Range[500], IntegerQ[# * DivisorSum[#, 1/DivisorSigma[0, #1] &]] &] (* Amiram Eldar, Feb 19 2021 *)

PARI

isok(k) = denominator(k*sumdiv(k, d, 1/numdiv(d))) == 1; \\ Michel Marcus, Feb 15 2021

Formula

Numbers k such that k*Sum_{d|k} 1/A000005(d) is an integer.