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.

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, 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, 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

Offset: 1

Author

Labos Elemer, Jun 04 2002

Keywords

• nonn

Comments

p^2 and 2p^2 are always in inverse set, so a(n) >= 2.

Examples

			For n = 5: prime(5) = 11, a(5) = 2 because InvPhi(110) = {121, 242}.
For n = 6: prime(6) = 13, a(6) = 7 because InvPhi(13*12) = InvPhi(156) = {157, 169, 237, 314, 316, 338, 474}.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A036689, A000010.

Programs

Maple

[seq(nops(invphi(ithprime(j)*(-1+ithprime(j)))),j=1..128)];

PARI

a(n) = my(p=prime(n)); #invphi(p*(p-1)); \\ Michel Marcus, Mar 25 2020

Formula

a(n) = Card[InvPhi(p(n)*(p(n)-1))] = Card[InvPhi(A036689(n))].