

A110590


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


1




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



