A071707 Numbers k that divide tau(k)*sigma(k).

1, 2, 6, 12, 18, 24, 28, 40, 84, 120, 224, 234, 240, 252, 360, 468, 496, 672, 864, 936, 1638, 1920, 2016, 2480, 3276, 4320, 4680, 6048, 6528, 6552, 7440, 8128, 9360, 10880, 22320, 22932, 26208, 30240, 32640, 32760, 47616, 56896, 58752, 65520, 74880, 79360, 84480

Offset: 1

Author

Reinhard Zumkeller, Jun 03 2002

Keywords

• nonn

Examples

			The divisors of 18 are {1,2,3,6,9,18}, so tau(18) = 6 and sigma(18) = 1+2+3+6+9+18 = 39, 18 is a term as 18*13 = 6*39 = tau(18)*sigma(18).
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..300

Crossrefs

A007691 is a subsequence.

Cf. A064840 (A000005(n)*A000203(n)).

Programs

Mathematica

Select[Range[10^5], Divisible[Times @@ DivisorSigma[{0, 1}, #], #] &] (* Amiram Eldar, Apr 16 2025 *)

PARI

isok(k) = {my(f = factor(k)); !((numdiv(f) * sigma(f)) % k);} \\ Amiram Eldar, Apr 16 2025