A241480 Numbers k such that the GCD of the x's that satisfy sigma(x) = sigma(k) is not equal to 1.

2, 3, 4, 5, 7, 8, 9, 12, 13, 18, 19, 22, 27, 29, 32, 36, 37, 43, 45, 48, 49, 50, 61, 64, 67, 68, 72, 73, 75, 80, 81, 82, 91, 98, 100, 101, 104, 106, 109, 116, 121, 122, 128, 129, 133, 134, 137, 144, 146, 148, 149, 152, 156, 157, 160, 162, 163, 169, 171, 173

Offset: 1

Author

Michel Marcus, Apr 23 2014

Keywords

• nonn

Comments

Apart from 1, all terms of A211656 belong here since the solutions to sigma(x)=sigma(n) form a singleton and thus their GCD is n itself.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000203, A211656, A241479.

Programs

PARI

sigv(n) =  select(i->sigma(i) == n, vector(n, i, i));
isok(n) = (gcd(sigv(sigma(n))) != 1);

PARI

is(k) = gcd(invsigma(sigma(k))) > 1; \\ Amiram Eldar, Dec 19 2024, using Max Alekseyev's invphi.gp

Formula

Numbers k such that A241479(k) is not equal to 1.