A356453 Numbers k such that 2*k^2 is not in A014567; complement of A356449.

3, 6, 9, 10, 12, 15, 18, 21, 24, 27, 28, 30, 33, 36, 39, 40, 42, 45, 48, 50, 51, 54, 57, 60, 63, 66, 69, 70, 72, 75, 77, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 110, 111, 114, 117, 120, 123, 126, 129, 130, 132, 133, 135, 136, 138, 140, 141, 144, 147, 150, 153, 154, 155

Offset: 1

Author

Jianing Song, Aug 07 2022

Keywords

• nonn
• easy

Comments

Numbers k such that k and sigma(2*k^2) are not coprime, sigma = A000203.

Includes all multiples of 3 since 3 divides sigma(m) if m is twice a square (cf. A065766).

Examples

			10 is a term since 10 and sigma(2*10^2) = 465 have a common factor 5.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..8914 (all terms <= 20000)

Crossrefs

Cf. A014567, A000203, A356448, A356449, A356452, A356454, A356456 (all multiples of 3 removed), A065766.

Programs

Mathematica

Select[Range[155],GCD[#, DivisorSigma[1,2#^2]]>1 &] (* Stefano Spezia, Aug 07 2024 *)

PARI

isA356453(n) = gcd(n, sigma(2*n^2))>1