A356456 Numbers k not divisible by 3 such that 2*k^2 is not in A014567.

10, 28, 40, 50, 70, 77, 110, 130, 133, 136, 140, 154, 155, 160, 161, 170, 176, 190, 196, 200, 209, 224, 230, 250, 259, 266, 275, 280, 290, 308, 310, 322, 350, 364, 370, 371, 377, 385, 410, 416, 418, 430, 440, 469, 470, 476, 490, 496, 518, 520, 530, 532, 539, 550, 553, 590

Offset: 1

Author

Jianing Song, Aug 07 2022

Keywords

• nonn
• easy

Comments

Numbers k not divisible by 3 such that k and sigma(2*k^2) are not coprime, sigma = A000203.

Note that if m is twice a square, then sigma(m) is divisible by 3 (cf. A065766).

Examples

			28 is a term since 28 and sigma(2*28^2) = 3591 have a common factor 7, and 28 is not divisible by 3.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..11669 (all terms <= 100000)

Crossrefs

Cf. A014567, A000203, A065766.

Equals A356453 \ A008585.

Programs

PARI

isA356456(n) = (n%3) && gcd(n, sigma(2*n^2))>1