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Numbers k such that the sum of the squares of the divisors of k (A001157(k)) is squarefree.
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%I #24 Jan 11 2025 19:56:19

%S 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,

%T 44,47,48,49,50,52,53,58,59,61,62,64,67,68,71,72,73,75,76,79,80,83,88,

%U 89,92,97,98,99,101,103,109,113,116,117,118,121,122,124,127,128,131,137

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

%C 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

%H Amiram Eldar, <a href="/A080401/b080401.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)

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

%p select(n -> numtheory:-issqrfree(numtheory:-sigma[2](n)), [$1..1000]); # _Robert Israel_, Mar 29 2019

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

%t Select[Range[200],SquareFreeQ[DivisorSigma[2,#]]&] (* _Harvey P. Dale_, Jun 17 2014 *)

%o (PARI) isok(n) = issquarefree(sigma(n, 2)); \\ _Michel Marcus_, Mar 29 2019

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

%K nonn

%O 1,2

%A _Labos Elemer_, Mar 19 2003