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Numbers k such that the number of divisors of k and sum of cubes of divisors of k are relatively prime.
7

%I #16 May 08 2021 22:55:42

%S 1,2,4,8,9,16,25,36,81,100,121,128,144,162,225,256,289,324,400,484,

%T 512,529,625,729,841,900,1024,1089,1156,1250,1296,1458,1681,1936,2025,

%U 2116,2209,2304,2401,2500,2601,2809,2916,3025,3364,3481,3600,4096,4356,4624

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

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

%H Amiram Eldar, <a href="/A046680/b046680.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[5000], CoprimeQ[DivisorSigma[0, #], DivisorSigma[3, #]] &] (* _Amiram Eldar_, Aug 08 2019 *)

%o (PARI) isok(n) = gcd(numdiv(n), sigma(n, 3)) == 1; \\ _Michel Marcus_, Sep 24 2019

%Y Cf. A028982, A046678, A046679, A046681, A046683, A046685.

%K nonn

%O 1,2

%A _Labos Elemer_