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
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
KEYWORD
nonn,more
AUTHOR
Walter Kehowski, Sep 13 2005
STATUS
approved