A110590 Balanced numbers k (A020492) such that phi(k) is not divisible by 12.

1, 2, 3, 6, 12, 14, 15, 30, 264, 3828

Offset: 1

Author

Walter Kehowski, Sep 13 2005

Keywords

• nonn
• more

Comments

The only balanced numbers k such that sigma(k) is not divisible by 12 are 1, 2, 3.

a(11) if it exists is greater than 10^8. - Michel Marcus, Aug 06 2013

a(11) if it exists is greater than 10^13. - Giovanni Resta, Jul 13 2015

a(11) if it exists is greater than 6.5*10^14 (checked using data from Jud McCranie). - Amiram Eldar, Nov 10 2024

Crossrefs

Cf. A000010, A000203, A020492.

Programs

Maple

with(numtheory): BNM:=[]: for z from 1 to 1 do for n from 1 to 100000 do if phi(n) mod 12 > 0 and sigma(n) mod phi(n) = 0 then BNM:=[op(BNM),n] fi; od; od; BNM; # after 3828 there are no others up to 2*10^6.

Mathematica

fQ[n_] := Block[{ds = DivisorSigma[1, n], ep = EulerPhi@n}, Mod[ep, 12] > 0 && IntegerQ[ds/ep]]; Do[ If[ fQ@n, Print@n], {n, 4*10^8}] (* Robert G. Wilson v, Jun 19 2006 *)

Formula

k such that sigma(k)/phi(k) is an integer and phi(k) mod 12 != 0.