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Numbers k such that the number of divisors of k and sum of squares of divisors of k are relatively prime.
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%I #20 May 09 2021 02:17:22

%S 1,2,8,9,16,18,64,72,81,128,144,625,729,1024,1152,1296,1458,2401,4096,

%T 5184,5625,5832,6561,8192,9216,10000,11664,13122,15625,21609,28561,

%U 31250,32768,38416,40000,46656,50625,52488,59049,65536,83521,90000

%N Numbers k such that the number of divisors of k and sum of squares of divisors of k are relatively prime.

%C It can be shown that this is a subsequence of A028982.

%H Amiram Eldar, <a href="/A046679/b046679.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[91000],CoprimeQ[DivisorSigma[0,#], DivisorSigma[2,#]]&] (* _Harvey P. Dale_, May 11 2011 *)

%o (PARI) isok(n) = gcd(sigma(n, 2), numdiv(n)) == 1; \\ _Michel Marcus_, Sep 24 2019

%Y Cf. A028982, A046678, A046680, A046681, A046683, A046685.

%K nonn

%O 1,2

%A _Labos Elemer_

%E a(1)=1 added by _Amiram Eldar_, Sep 24 2019