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A072006 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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..98.

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: invphi.gp, 2005-2019.

FORMULA

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

EXAMPLE

n=5: p(5)=11, a(5)=2 because InvPhi(110) = {121, 242}.

n=6: p(6)=13, a(6)=7 because InvPhi(13.12) = InvPhi(156)= {157, 169, 237, 314, 316, 338, 474}.

MAPLE

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

PROG

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

CROSSREFS

Cf. A036689, A000010.

Sequence in context: A100394 A178783 A156671 * A014238 A275719 A014250

Adjacent sequences:  A072003 A072004 A072005 * A072007 A072008 A072009

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 04 2002

STATUS

approved

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Last modified April 16 23:40 EDT 2021. Contains 343051 sequences. (Running on oeis4.)