A073750 Factors of 2 in the denominators of the fractional coefficients of the square-root of the prime power series: sum_{n=0..inf} p_n x^n, where p_n is the n-th prime and p_0 is defined to be 1.

0, 0, 0, 1, 1, 1, 3, 3, 3, 4, 4, 4, 7, 7, 7, 8, 8, 8, 10, 10, 10, 11, 11, 11, 15, 15, 15, 16, 16, 16, 18, 18, 18, 19, 19, 19, 22, 22, 22, 23, 23, 23, 25, 25, 25, 26, 26, 26, 31, 31, 31, 32, 32, 32, 34, 34, 34, 35, 35, 35, 38, 38, 38, 39, 39, 39, 41, 41, 41, 42, 42, 42

Offset

0,7

Comments

Are all the denominators exact powers of 2?

D_n=1 for all n <= 250. - Sean A. Irvine, Dec 17 2024

Links

Sean A. Irvine, Table of n, a(n) for n = 0..250

Formula

Convolution of Sum_{n=0..inf} A073749(n)/[D_n*2^{a(n)}] x^n yields the prime power series Sum_{n=0..inf} p_n x^n, where p_n is the n-th prime and p_0=1 and where D_n is a positive integer; D_n for the first 60 terms is 1 (is it always equal to 1?).

a(n) = A007814(denominator([x^n] sqrt(Sum_{k>=0} p_k * x^k))) with p_0=1. - Sean A. Irvine, Dec 17 2024

Crossrefs

Cf. A073749, A007814.

Sequence in context: A105590 A220845 A361469 * A378658 A270059 A120204

Adjacent sequences: A073747 A073748 A073749 * A073751 A073752 A073753

Keyword

easy,frac,nonn

Author

Paul D. Hanna, Aug 07 2002

Status

approved