A046686 -id:A046686 - cp's OEIS frontend

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

Labos Elemer

nonn

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

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.

Cf. A001159, A046684, A046686.

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

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

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

Original entry on oeis.org

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

Labos Elemer

nonn

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

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.

Cf. A001157, A046686, A046687.

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

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

cp's OEIS Frontend

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

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