A354954 - OEIS

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A354954

Decimal expansion of Sum_{p = primes} 1 / (p * log(p)^4).

2, 4, 4, 3, 2, 2, 7, 0, 4, 3, 5, 4, 4, 4, 1, 0, 1, 8, 8, 7, 2, 9, 6, 8, 3, 2, 9, 7, 3, 6, 9, 7, 3, 4, 5, 7, 6, 4, 6, 1, 4, 5, 3, 0, 8, 7, 7, 4, 0, 4, 0, 0, 4, 2, 8, 6, 6, 4, 6, 5, 1, 4, 8, 5, 2, 6, 7, 3, 5, 0, 8, 5, 9, 9, 6, 4, 5, 3, 2, 5, 5, 9, 4, 5, 7, 8, 7, 6, 9, 0, 3, 2, 6, 7, 0, 0, 9, 0, 6, 0, 1, 6, 7, 9, 2

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

R. J. Mathar, Twenty digits of some integrals of the prime zeta function, arXiv:0811.4739 (2008-2009).

EXAMPLE

2.443227043544410188729683297369734576461453087740400428664651485267350...

PROG

(PARI) default(realprecision, 200); s=0; for(k=1, 500, s = s + moebius(k)/(6*k^5) * intnum(x=k, [[1], 1], (x-k)^3 * log(zeta(x))); print(s));

CROSSREFS

Cf. A137245, A319231, A354917, A354953.