A339815 Let x = A019565(2*n); a(n) is the difference between 2-adic valuations of phi(x) and (x-1).

0, 0, 2, 0, 0, 2, 1, 0, -3, 2, 2, 0, 2, -3, 4, 0, 2, -2, 4, 2, 0, 4, 4, 2, 2, 4, 1, 1, 4, 4, 6, 0, 4, 4, 6, 4, 4, 6, 5, 4, 2, 6, 6, 4, 6, 4, 8, 4, 6, 4, 8, 6, 3, 8, 8, 6, 6, 8, 6, 5, 8, 8, 10, 0, -1, 2, 2, 0, 2, 1, 4, -2, 2, 2, 4, 2, 2, 4, 3, 2, 2, 4, 3, -2, 4, 4, 6, 2, 4, 2, 6, 4, 1, 6, 6, 4, 3, 6, 6, 4, 6, 5, 8, 1, 6

Offset: 1

Author

Antti Karttunen, Dec 18 2020

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000010, A007814, A019565, A339809, A339814, A339821, A339822.

Cf. A339816 (indices of terms < 1).

Programs

PARI

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A339815(n) = { my(x=A019565(2*n)); valuation(eulerphi(x),2)-valuation(x-1,2); };

Formula

a(n) = A339822(n) - A339814(n).

a(n) = A007814(A000010(A019565(2n))) - A007814(A019565(2n)-1).