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A072006
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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.
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0
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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
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OFFSET
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1,1
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COMMENTS
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p^2 and 2p^2 are always in inverse set, so a(n)>=2.
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LINKS
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FORMULA
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a(n) = Card[{InvPhi(p(n)*(p(n)-1)]} = Card[InvPhi(A036689(n)].
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EXAMPLE
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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}.
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MAPLE
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[seq(nops(invphi(ithprime(j)*(-1+ithprime(j)))), j=1..128)];
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PROG
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(PARI) a(n) = my(p=prime(n)); #invphi(p*(p-1)); \\ Michel Marcus, Mar 25 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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