|
%I #6 Mar 30 2012 17:37:42
%S 2,11,37,169,917,1087,15407,10379,30451,64591,187063,498419,1304707,
%T 3523969,9558541,26042629,73134517,189963073,528839387,1394194181,
%U 3779851321,10246935931,27800769133,75370121689
%N a(n) is the earliest number m such that n*pi(m)=phi(m).
%C It seems that for each n, a(n) exists and the set An={m|n*pi(m)=phi(m)} is finite, for example A1={2,3,4,8,10,14,20,90}(elements of A1 are terms of the sequence A037171), A2={11,13,27,39,63,122,124, 136,152,176,224,322,364,410,460,1086,1164,3432,3612},... . According to the definition, a(n) is the smallest element of An. For n<19, 3 doesn't divide a(n), is this true for all terms of the sequence?
%F a[n_]:=(For[m=1, n*PrimePi[m]!=EulerPhi[m], m++ ];m)
%e a(18)=189963073 because 18*pi(189963073)=phi(189963073) and for m<189963073 18*pi(m)!= phi(m).
%t a[n_]:=(For[m=1, n*PrimePi[m]!=EulerPhi[m], m++ ];m);Do[Print[a[n]], {n, 18}]
%Y Cf. A037171.
%K more,nonn
%O 1,1
%A _Farideh Firoozbakht_, Sep 07 2004
%E a(14) corrected and a(19)-a(24) from _Donovan Johnson_, May 03 2010
|
