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Numbers k such that the sum of the squares of the divisors of k (A001157(k)) is not squarefree.
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%I #15 Aug 12 2024 09:35:05

%S 6,7,14,15,21,24,26,27,28,30,33,34,35,36,39,41,42,43,45,46,51,54,55,

%T 56,57,60,63,65,66,69,70,74,77,78,81,82,84,85,86,87,90,91,93,94,95,96,

%U 100,102,104,105,106,107,108,110,111,112,114,115,119,120,123,125,126,129

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

%H Amiram Eldar, <a href="/A080402/b080402.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)

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

%t Do[s=MoebiusMu[DivisorSigma[2, n]]; If[Equal[s, 0], Print[n]], {n, 1, 1000}]

%t Select[Range[130],!SquareFreeQ[DivisorSigma[2,#]]&] (* _Harvey P. Dale_, Oct 10 2011 *)

%o (PARI) is(k) = !issquarefree(sigma(k, 2)); \\ _Amiram Eldar_, Aug 12 2024

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

%K nonn

%O 1,1

%A _Labos Elemer_, Mar 19 2003