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

1,2

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.

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A248648 A063577 A087058 * A063760 A238334 A130448

Adjacent sequences: A046656 A046657 A046658 * A046660 A046661 A046662

Keyword

nonn

Author

Labos Elemer

Status

approved