A303494 Decimal expansion of Sum_{p prime} log(p)/p^4.

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

Offset

0,2

Comments

The negated first derivative of the Prime Zeta function at 4.

Links

Table of n, a(n) for n=0..100.

R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 (2008) Table 3, s=4.

J. B. Rosser, L. Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. J. Math. 6 (1) (1962) 64-94, Table IV

Eric Weisstein's MathWorld, Prime Zeta Function

Wikipedia, Prime Zeta Function

Example

0.060607633350770063392230983709713378406382877461259843991127681734...

Mathematica

RealDigits[PrimeZetaP'[4], 10, 100][[1]]

Crossrefs

Decimal expansion of Sum_{p prime} log(p)/p^k: A136271 (k=2), A303493 (k=3), A303494 (k=4), A303495 (k=5), A303496 (k=6), A303497 (k=7), A303498 (k=8), A303499 (k=9).

Sequence in context: A158090 A010677 A021169 * A198368 A064373 A195290

Adjacent sequences: A303491 A303492 A303493 * A303495 A303496 A303497

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 25 2018

Status

approved