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Numbers whose sum of divisors and sum of cubes of divisors are relatively prime.
1

%I #23 Sep 24 2019 09:20:13

%S 1,4,9,25,36,100,121,225,289,484,529,841,900,1089,1156,1681,2116,2209,

%T 2601,2809,3364,3481,4356,4761,5041,6724,6889,7225,7569,7921,8836,

%U 10201,10404,11236,11449,12769,13225,13924,15129,17161,18769,19044

%N Numbers whose sum of divisors and sum of cubes of divisors are relatively prime.

%C It appears that (a) all the numbers are squares, (b) the number of divisors is a power of 3.

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

%H Amiram Eldar, <a href="/A046659/b046659.txt">Table of n, a(n) for n = 1..10000</a>

%e k=100 has 9 divisors whose sum is 217 = 7*31 and whose sum of cubes is 1149823 = 19*73*829; gcd(217, 1149823) = 1, so 100 is in the sequence.

%t Select[Range[20000],GCD[DivisorSigma[1,#],DivisorSigma[3,#]]==1&] (* _Harvey P. Dale_, Feb 19 2011 *)

%o (PARI) isok(n) = gcd(sigma(n), sigma(n, 3)) == 1; \\ _Michel Marcus_, May 14 2018

%Y Cf. A028982, A046679, A046680, A046681, A046683, A046685.

%K nonn

%O 1,2

%A _Labos Elemer_