A063667 - OEIS

%I #14 Nov 07 2018 21:46:56

%S 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 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 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 Number of solutions of EulerPhi(x) = 12n + 2.

%H Antti Karttunen, <a href="/A063667/b063667.txt">Table of n, a(n) for n = 0..100000</a>

%F a(n) = A014197(A017545(n)). - _Antti Karttunen_, Nov 07 2018

%e In 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 In range n <= 100000, there are 48 nonzero values. - _Antti Karttunen_, Nov 07 2018

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

%o (PARI)

%o 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(n) = A014197(2+(12*n)); \\ _Antti Karttunen_, Nov 07 2018

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

%K nonn

%O 0,1

%A _Labos Elemer_, Aug 22 2001

%E Term a(0) = 3 prepended by _Antti Karttunen_, Nov 07 2018