A339814 - OEIS

%I #7 Dec 19 2020 07:59:50

%S 1,2,1,1,2,1,3,1,5,1,2,2,1,7,1,2,1,6,1,1,4,1,2,1,2,1,5,3,1,2,1,4,1,2,

%T 1,1,2,1,3,1,4,1,2,2,1,4,1,2,1,4,1,1,5,1,2,1,2,1,4,3,1,2,1,1,3,1,2,2,

%U 1,3,1,4,1,2,1,1,2,1,3,1,2,1,3,6,1,2,1,2,1,4,1,1,5,1,2,1,3,1,2,2,1,3,1,5,1

%N The exponent of the highest power of 2 dividing (A019565(2n) - 1).

%C The 2-adic valuation of A339809(2n).

%H Antti Karttunen, <a href="/A339814/b339814.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A007814(A339809(2*n)) = A007814(A019565(2*n)-1).

%F a(n) = A007814(A003961(A019565(n))-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 A339814(n) = valuation((A019565(2*n)-1),2);

%Y Bisection of A339813.

%Y Cf. A003961, A007814, A019565, A339809, A339815, A339822.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 18 2020