A073749 Numerators 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.

1, 1, 1, 3, 3, 5, 11, 19, 7, 39, 39, 37, 243, 451, -149, 845, 237, 1507, -1569, 8599, -7037, 22543, -27921, 45765, -630845, 1283427, -1552973, 4462097, -6470191, 8313975, -43768763, 67084957, -86965863, 247812897, -351911967, 477950179, -5373020297, 7552589095, -10293397313, 29278400177

Offset

0,4

Links

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

Formula

Convolution of Sum_{n=0..inf} A073749(n) / 2^A073750(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. [Corrected by Sean A. Irvine, Dec 17 2024]

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

Crossrefs

Cf. A073750.

Sequence in context: A261962 A301500 A084656 * A299590 A250396 A201866

Adjacent sequences: A073746 A073747 A073748 * A073750 A073751 A073752

Keyword

easy,frac,sign

Author

Paul D. Hanna, Aug 07 2002

Status

approved