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

1,2

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A001157, A046686, A046687.

Sequence in context: A358378 A062491 A087092 * A082377 A166401 A329131

Adjacent sequences: A046681 A046682 A046683 * A046685 A046686 A046687

Keyword

nonn

Author

Labos Elemer

Status

approved