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

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

Offset

1,2

Comments

The only balanced numbers such that sigma(n) 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

Links

Table of n, a(n) for n=1..10.

Formula

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

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 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 *)

Crossrefs

Cf. A000010, A000203, A020492.

Sequence in context: A015765 A015771 A020492 * A329401 A291174 A281110

Adjacent sequences: A110587 A110588 A110589 * A110591 A110592 A110593

Keyword

nonn,more

Author

Walter Kehowski, Sep 13 2005

Status

approved