A080401 A001157(n) is squarefree: sum of squares of divisors of n 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

1,2

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Abs[mu[sigma[2, a(n)]]]=1.

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 *)

Prog

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

Crossrefs

Cf. A001157, A005117, A065300.

Sequence in context: A047602 A039076 A037471 * A288666 A180734 A031482

Adjacent sequences: A080398 A080399 A080400 * A080402 A080403 A080404

Keyword

nonn

Author

Labos Elemer, Mar 19 2003

Status

approved