A103113 - OEIS

%I #14 Sep 13 2014 07:52:03

%S 1,113125,2322432,21332611,2115124224,3111423252,3412115322,

%T 12451223232,116222114125,1141433232511,2231521231226,2334121141253,

%U 3222154622111,4211413132352,15123362231122,21123234615111,32125124213611,114231133412352,233152112133612

%N Numbers n such that phi(n)=phi(d_1^d_1)*phi(d_2^d_2)*...*phi(d_k^d_k) where d_1 d_2 ... d_k is the decimal expansion of n.

%C a(38) (if it exists) >= 10^18. - _Hiroaki Yamanouchi_, Sep 10 2014

%H Hiroaki Yamanouchi, <a href="/A103113/b103113.txt">Table of n, a(n) for n = 1..37</a>

%e 21332611 is in the sequence because phi(21332611)=phi(2^2)*phi(1^1)*phi(3^3)*phi(3^3)*phi(2^2)*phi(6^6)*phi(1^1)*phi(1^1).

%t Do[h=IntegerDigits[m];l=Length[h];If[Min[h]>0&&EulerPhi[m]== Product[EulerPhi[h[[k]]^h[[k]]], {k, l}], Print[m]], {m, 200000000}]

%Y Cf. A104898.

%K nonn,base

%O 1,2

%A _Farideh Firoozbakht_, Mar 29 2005

%E a(5)-a(17) from _Max Alekseyev_, May 10 2009, May 05 2010, Aug 22 2013

%E a(18)-a(19) from _Hiroaki Yamanouchi_, Sep 10 2014