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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.
4
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
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
Sequence in context: A105590 A220845 A361469 * A378658 A270059 A120204
KEYWORD
easy,frac,nonn
AUTHOR
Paul D. Hanna, Aug 07 2002
STATUS
approved