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

1,1

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).

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A055264 A113502 A229307 * A061904 A206284 A372850

Adjacent sequences: A356450 A356451 A356452 * A356454 A356455 A356456

Keyword

nonn,easy

Author

Jianing Song, Aug 07 2022

Status

approved