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.

1, 2, 4, 8, 9, 18, 25, 100, 121, 225, 289, 484, 529, 841, 1089, 1156, 1681, 2116, 2209, 2601, 2809, 3364, 3481, 4761, 5041, 6724, 6889, 7225, 7569, 7921, 8836, 10201, 11236, 11449, 12769, 13225, 13924, 15129, 17161, 18769, 19881, 20164, 21025

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

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

From Robert Israel, Jul 09 2018: (Start)

The only terms that are not in A062503 are 2, 8 and 18.

No term is divisible by a term of A002476.

p^2 is a term for every p in A003627. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Mathematics StackExchange, Are 1+p^3+p^6 and 1+p^4+p^8 coprime?

Crossrefs

Cf. A002476, A003627, A028982, A046678, A046679, A046680, A046681, A046683, A062503.

Programs

Maple

N:= 10^6: # to get all terms <= N
sort(select(filter, [seq(t^2,t=1..isqrt(N)),seq(2*t^2,t=1..isqrt(N/2))])); # Robert Israel, Jul 09 2018

Mathematica

Select[Range[25000], CoprimeQ[DivisorSigma[3, #], DivisorSigma[4, #]] &] (* Michael De Vlieger, Aug 10 2023 *)

PARI

isok(n) = gcd(sigma(n, 3), sigma(n, 4)) == 1; \\ Michel Marcus, Sep 24 2019