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%I #19 Jan 17 2020 05:06:03
%S 0,0,3,1,3,4,11,17,116,25,222,1806,54,223,302422,213,35,320146,8,1403
%N a(n) is the number of n-digit numbers m such that phi(m)=phi(10^n+1), gcd(10^n+1,m)=1 and 10 doesn't divide m.
%C If 10^n+1 is prime (n must be of the form 2^k) then a(n)=0 because in this case there is no n-digit number m such that phi(10^n+1) = 10^n = phi(m). I defined this sequence and sequences A147547 and A147548 to answer a question (Nov 06 2008) from _M. F. Hasler_ about the infiniteness of the "primitive" elements (those that aren't multiples of 10) of sequence A147619.
%t a[n_]:=(b=10^n+1;c=EulerPhi[b];e=b-2; If[PrimeQ[b],0,Length[Select[Range[ c+1,e],Mod[ #,10]>0 && GCD[ #,b]==1 && EulerPhi[b]==EulerPhi[ # ]&]]]); Do[Print[a[n]],{n,9}]
%Y Cf. A147547, A147548.
%K nonn,base,hard,more
%O 1,3
%A _Farideh Firoozbakht_, Nov 12 2008
%E a(10)-a(14) from _Max Alekseyev_, Mar 12 2009
%E a(15)-a(20) from _Hiroaki Yamanouchi_, Aug 27 2014