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

1,2

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?

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 *)

Prog

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

Crossrefs

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

Sequence in context: A255717 A354973 A177404 * A248741 A140141 A088274

Adjacent sequences: A046682 A046683 A046684 * A046686 A046687 A046688

Keyword

nonn

Author

Labos Elemer

Status

approved