A080401 Numbers k such that the sum of the squares of the divisors of k (A001157(k)) is squarefree.

1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 22, 23, 25, 29, 31, 32, 37, 38, 40, 44, 47, 48, 49, 50, 52, 53, 58, 59, 61, 62, 64, 67, 68, 71, 72, 73, 75, 76, 79, 80, 83, 88, 89, 92, 97, 98, 99, 101, 103, 109, 113, 116, 117, 118, 121, 122, 124, 127, 128, 131, 137

Offset: 1

Author

Labos Elemer, Mar 19 2003

Keywords

• nonn

Comments

If m*k is in the sequence with m and k coprime, then m and k must be in the sequence. - Robert Israel, Mar 29 2019

Links

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

Crossrefs

Cf. A001157, A005117, A065300, A080402 (complement).

Programs

Maple

select(n -> numtheory:-issqrfree(numtheory:-sigma[2](n)), [$1..1000]); # Robert Israel, Mar 29 2019

Mathematica

Do[s=MoebiusMu[DivisorSigma[2, n]]; If[ !Equal[s, 0], Print[n]], {n, 1, 1000}]
Select[Range[200],SquareFreeQ[DivisorSigma[2,#]]&] (* Harvey P. Dale, Jun 17 2014 *)

PARI

isok(n) = issquarefree(sigma(n, 2)); \\ Michel Marcus, Mar 29 2019

Formula

abs(mu(sigma_2(a(n)))) = 1.