A356449 Numbers k such that 2*k^2 is in A014567.

1, 2, 4, 5, 7, 8, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 29, 31, 32, 34, 35, 37, 38, 41, 43, 44, 46, 47, 49, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103, 104, 106, 107, 109, 112, 113

Offset

1,2

Comments

Numbers k such that k and sigma(2*k^2) are coprime, sigma = A000203.

No term can be a multiple 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..11086 (all terms <= 20000)

Example

20 is a term since 20 and sigma(2*20^2) = 1953 are coprime.

Mathematica

q[k_] := CoprimeQ[2*k^2, DivisorSigma[1, 2*k^2]]; Select[Range[120], q] (* Amiram Eldar, Mar 16 2026 *)

Prog

(PARI) isA356449(n) = gcd(n, sigma(2*n^2))==1

Crossrefs

Cf. A014567, A000203, A356382, A356448, A356451, A356453 (complement), A065766.

Sequence in context: A368364 A290334 A206285 * A229303 A262978 A112886

Adjacent sequences: A356446 A356447 A356448 * A356450 A356451 A356452

Keyword

nonn,easy

Author

Jianing Song, Aug 07 2022

Status

approved