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A046685 Numbers k such that the sum of cubes of divisors of k and the sum of 4th powers of divisors of k are relatively prime.

%I A046685 #21 Aug 11 2023 10:00:30
%S A046685 1,2,4,8,9,18,25,100,121,225,289,484,529,841,1089,1156,1681,2116,2209,
%T A046685 2601,2809,3364,3481,4761,5041,6724,6889,7225,7569,7921,8836,10201,
%U A046685 11236,11449,12769,13225,13924,15129,17161,18769,19881,20164,21025
%N A046685 Numbers k such that the sum of cubes of divisors of k and the sum of 4th powers of divisors of k are relatively prime.
%C A046685 It can be shown that this is a subsequence of A028982.
%C A046685 From _Robert Israel_, Jul 09 2018: (Start)
%C A046685 The only terms that are not in A062503 are 2, 8 and 18.
%C A046685 No term is divisible by a term of A002476.
%C A046685 p^2 is a term for every p in A003627. (End)
%H A046685 Robert Israel, <a href="/A046685/b046685.txt">Table of n, a(n) for n = 1..10000</a>
%H A046685 Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/2846047/are-1p3p6-and-1p4p8-coprime">Are 1+p^3+p^6 and 1+p^4+p^8 coprime?</a>
%p A046685 N:= 10^6: # to get all terms <= N
%p A046685 sort(select(filter, [seq(t^2,t=1..isqrt(N)),seq(2*t^2,t=1..isqrt(N/2))])); # _Robert Israel_, Jul 09 2018
%t A046685 Select[Range[25000], CoprimeQ[DivisorSigma[3, #], DivisorSigma[4, #]] &] (* _Michael De Vlieger_, Aug 10 2023 *)
%o A046685 (PARI) isok(n) = gcd(sigma(n, 3), sigma(n, 4)) == 1; \\ _Michel Marcus_, Sep 24 2019
%Y A046685 Cf. A002476, A003627, A028982, A046678, A046679, A046680, A046681, A046683, A062503.
%K A046685 nonn
%O A046685 1,2
%A A046685 _Labos Elemer_