cp's OEIS Frontend

A072006 Number of terms in InversePhi set of prime(n)*(prime(n)-1) = phi(p(n)^2), where prime(n) is the n-th prime and phi=A000010.

%I A072006 #22 Mar 18 2025 07:32:45
%S A072006 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 A072006 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 A072006 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 A072006 Number of terms in InversePhi set of prime(n)*(prime(n)-1) = phi(p(n)^2), where prime(n) is the n-th prime and phi=A000010.
%C A072006 p^2 and 2p^2 are always in inverse set, so a(n) >= 2.
%H A072006 Amiram Eldar, <a href="/A072006/b072006.txt">Table of n, a(n) for n = 1..10000</a>
%H A072006 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%F A072006 a(n) = Card[InvPhi(p(n)*(p(n)-1))] = Card[InvPhi(A036689(n))].
%e A072006 For n = 5: prime(5) = 11, a(5) = 2 because InvPhi(110) = {121, 242}.
%e A072006 For n = 6: prime(6) = 13, a(6) = 7 because InvPhi(13*12) = InvPhi(156) = {157, 169, 237, 314, 316, 338, 474}.
%p A072006 [seq(nops(invphi(ithprime(j)*(-1+ithprime(j)))),j=1..128)];
%o A072006 (PARI) a(n) = my(p=prime(n)); #invphi(p*(p-1)); \\ _Michel Marcus_, Mar 25 2020
%Y A072006 Cf. A036689, A000010.
%K A072006 nonn
%O A072006 1,1
%A A072006 _Labos Elemer_, Jun 04 2002