A046687 Numbers k such that k and sum of 4th powers of divisors of k are relatively prime.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 18, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43, 45, 47, 49, 50, 51, 53, 55, 57, 59, 61, 64, 65, 67, 69, 71, 72, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 98, 99, 100, 101, 103, 105, 107, 109, 111, 113, 115, 119

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..10076

Robert E. Dressler, On a theorem of Niven, Canadian Mathematical Bulletin, Vol. 17, No. 1 (1974), pp. 109-110.

Mathematica

Select[Range[120], GCD[#, DivisorSigma[4, #]] == 1 &] (* Ivan Neretin, Dec 30 2015 *)
Select[Range[150], CoprimeQ[#, DivisorSigma[4, #]]&] (* Harvey P. Dale, Jan 15 2024 *)

Prog

(PARI) isok(n) = gcd(n, sigma(n, 4))  == 1; \\ Michel Marcus, Dec 20 2013

Crossrefs

Cf. A001159, A046684, A046686.

Sequence in context: A191848 A360613 A293205 * A175418 A078175 A213715

Adjacent sequences: A046684 A046685 A046686 * A046688 A046689 A046690

Keyword

nonn

Author

Labos Elemer

Status

approved