A063667 Number of solutions of phi(x) = 12n + 2.

3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,1

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Formula

a(n) = A014197(A017545(n)). - Antti Karttunen, Nov 07 2018

Example

In the range n=0..10000, only 18 invphi(12n + 2) sets are nonempty, always with 2 terms. E.g., n = 8034, a(8034) = 2 because 12*8034 + 2 = 96410 and invphi(96410) = {96721,193442}. - Original comment corrected by Antti Karttunen, Nov 07 2018
In the range n <= 100000, there are 48 nonzero values. - Antti Karttunen, Nov 07 2018

Maple

with(numtheory): [seq(nops(invphi(2+12*j)), j=0..10000)];

Prog

(PARI)
A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))}; \\ From A014197 by M. F. Hasler
A063667(n) = A014197(2+(12*n)); \\ Antti Karttunen, Nov 07 2018
(PARI) a(n) = invphiNum(12*n+2); \\ Amiram Eldar, Nov 29 2024, using Max Alekseyev's invphi.gp

Crossrefs

Cf. A000010, A002202, A005277, A014197, A017545.

Sequence in context: A030121 A320659 A062535 * A171063 A308229 A318673

Adjacent sequences: A063664 A063665 A063666 * A063668 A063669 A063670

Keyword

nonn

Author

Labos Elemer, Aug 22 2001

Extensions

Term a(0) = 3 prepended by Antti Karttunen, Nov 07 2018

Status

approved