A046659 Numbers whose sum of divisors and sum of cubes of divisors are relatively prime.

1, 4, 9, 25, 36, 100, 121, 225, 289, 484, 529, 841, 900, 1089, 1156, 1681, 2116, 2209, 2601, 2809, 3364, 3481, 4356, 4761, 5041, 6724, 6889, 7225, 7569, 7921, 8836, 10201, 10404, 11236, 11449, 12769, 13225, 13924, 15129, 17161, 18769, 19044

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

Select[Range[20000],GCD[DivisorSigma[1,#],DivisorSigma[3,#]]==1&]  (* Harvey P. Dale, Feb 19 2011 *)

PARI

isok(n) = gcd(sigma(n), sigma(n, 3)) == 1; \\ Michel Marcus, May 14 2018