A080402 Numbers k such that the sum of the squares of the divisors of k (A001157(k)) is not squarefree.

6, 7, 14, 15, 21, 24, 26, 27, 28, 30, 33, 34, 35, 36, 39, 41, 42, 43, 45, 46, 51, 54, 55, 56, 57, 60, 63, 65, 66, 69, 70, 74, 77, 78, 81, 82, 84, 85, 86, 87, 90, 91, 93, 94, 95, 96, 100, 102, 104, 105, 106, 107, 108, 110, 111, 112, 114, 115, 119, 120, 123, 125, 126, 129

Offset: 1

Author

Labos Elemer, Mar 19 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A001157, A005117, A013929, A065300, A080401 (complement).

Programs

Mathematica

Do[s=MoebiusMu[DivisorSigma[2, n]]; If[Equal[s, 0], Print[n]], {n, 1, 1000}]
Select[Range[130],!SquareFreeQ[DivisorSigma[2,#]]&] (* Harvey P. Dale, Oct 10 2011 *)

PARI

is(k) = !issquarefree(sigma(k, 2)); \\ Amiram Eldar, Aug 12 2024

Formula

mu(sigma_2(a(n))) = 0.