A046686 Numbers k such that k and sum of cubes of divisors of k are relatively prime.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 36, 37, 39, 41, 43, 47, 49, 50, 53, 55, 57, 59, 61, 63, 64, 65, 67, 71, 73, 75, 77, 79, 81, 83, 85, 89, 93, 97, 98, 100, 101, 103, 107, 109, 111, 113, 115, 117, 121, 125, 127, 128, 129, 131, 137, 139, 143

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

All even terms are either squares or doubled squares. - Ivan Neretin, Dec 30 2015

The asymptotic density of this sequence is 0 (Dressler, 1974). - Amiram Eldar, Jul 23 2020

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Robert E. Dressler, On a theorem of Niven, Canadian Mathematical Bulletin, Vol. 17, No. 1 (1974), pp. 109-110.

Crossrefs

Cf. A001158, A046684, A046687.

Programs

Mathematica

Select[Range[143], GCD[#, DivisorSigma[3, #]] == 1 &] (* Ivan Neretin, Dec 30 2015 *)