cp's OEIS Frontend

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

%I A063667 #18 Nov 29 2024 19:08:57
%S A063667 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,
%T A063667 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,
%U A063667 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
%N A063667 Number of solutions of phi(x) = 12n + 2.
%H A063667 Antti Karttunen, <a href="/A063667/b063667.txt">Table of n, a(n) for n = 0..100000</a>
%H A063667 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%F A063667 a(n) = A014197(A017545(n)). - _Antti Karttunen_, Nov 07 2018
%e A063667 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
%e A063667 In the range n <= 100000, there are 48 nonzero values. - _Antti Karttunen_, Nov 07 2018
%p A063667 with(numtheory): [seq(nops(invphi(2+12*j)),j=0..10000)];
%o A063667 (PARI)
%o A063667 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_
%o A063667 A063667(n) = A014197(2+(12*n)); \\ _Antti Karttunen_, Nov 07 2018
%o A063667 (PARI) a(n) = invphiNum(12*n+2); \\ _Amiram Eldar_, Nov 29 2024, using _Max Alekseyev_'s invphi.gp
%Y A063667 Cf. A000010, A002202, A005277, A014197, A017545.
%K A063667 nonn
%O A063667 0,1
%A A063667 _Labos Elemer_, Aug 22 2001
%E A063667 Term a(0) = 3 prepended by _Antti Karttunen_, Nov 07 2018