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%I #9 Mar 25 2020 15:07:45
%S 3,4,5,4,2,7,5,2,2,2,2,6,10,2,2,2,2,7,4,2,16,4,2,8,19,5,2,2,2,13,2,2,
%T 2,4,5,4,2,4,2,5,2,14,2,21,2,2,2,2,2,5,5,2,28,2,2,2,2,2,8,8,2,2,2,2,4,
%U 5,2,14,2,7,5,2,2,5,4,2,2,11,7,17,2,11,2,26,2,2,12,4,5,2,2,2,2,2,2,2,5,5
%N Number of terms in InversePhi set of p(n)*(p(n)-1) = phi(p(n)^2), where p(n) is the n-th prime and phi=A000010.
%C p^2 and 2p^2 are always in inverse set, so a(n)>=2.
%H Max Alekseyev, <a href="https://home.gwu.edu/~maxal/gpscripts/invphi.gp">PARI/GP Scripts for Miscellaneous Math Problems: invphi.gp</a>, 2005-2019.
%F a(n) = Card[{InvPhi(p(n)*(p(n)-1)]} = Card[InvPhi(A036689(n)].
%e n=5: p(5)=11, a(5)=2 because InvPhi(110) = {121, 242}.
%e n=6: p(6)=13, a(6)=7 because InvPhi(13.12) = InvPhi(156)= {157, 169, 237, 314, 316, 338, 474}.
%p [seq(nops(invphi(ithprime(j)*(-1+ithprime(j)))),j=1..128)];
%o (PARI) a(n) = my(p=prime(n)); #invphi(p*(p-1)); \\ _Michel Marcus_, Mar 25 2020
%Y Cf. A036689, A000010.
%K nonn
%O 1,1
%A _Labos Elemer_, Jun 04 2002
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