A046684 Numbers k such that k and sum of squares of divisors of k are relatively prime.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 18, 19, 21, 23, 25, 27, 29, 31, 32, 33, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 64, 67, 69, 71, 72, 73, 77, 79, 81, 83, 87, 89, 91, 93, 95, 97, 98, 99, 100, 101, 103, 107, 109, 111, 113, 119, 121, 123, 125, 127, 128, 129

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. A001157, A046686, A046687.

Programs

Mathematica

Select[Range[130], GCD[#, DivisorSigma[2, #]] == 1 &] (* Ivan Neretin, Dec 30 2015 *)

PARI

isok(n) = gcd(n, sigma(n, 2)) == 1; \\ Michel Marcus, Jan 10 2017