A080401 -id:A080401 - cp's OEIS frontend

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

Labos Elemer, Mar 19 2003

nonn

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

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

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 *)

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

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

A080403 Numbers n such that both A000203(n) and A001157(n) are squarefree: sum of divisors and squares of divisors of n are squarefree.

Original entry on oeis.org

1, 2, 4, 5, 8, 9, 13, 16, 18, 20, 25, 29, 37, 49, 50, 61, 64, 72, 73, 80, 101, 109, 113, 116, 117, 121, 122, 128, 137, 144, 148, 169, 173, 181, 200, 208, 218, 229, 242, 244, 261, 277, 281, 289, 292, 313, 317, 320, 325, 333, 353, 362, 373, 389, 397, 401, 404, 409

Offset: 1

Labos Elemer, Mar 19 2003

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001157, A000203, A065300, A080401, A080402.

Do[s1=MoebiusMu[DivisorSigma[1, n]]; s2=MoebiusMu[DivisorSigma[2, n]]; If[ !Equal[s1, 0]&&!Equal[s2, 0], Print[n]], {n, 1, 1000}]

cp's OEIS Frontend

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

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