A339815 - OEIS

%I #10 Dec 24 2020 21:22:02

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A339815/b339815.txt">Table of n, a(n) for n = 1..65537</a>

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

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

%o (PARI)

%o A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };

%o A339815(n) = { my(x=A019565(2*n)); valuation(eulerphi(x),2)-valuation(x-1,2); };

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

%Y Cf. A339816 (indices of terms < 1).

%K sign

%O 1,3

%A _Antti Karttunen_, Dec 18 2020