A303496 Decimal expansion of Sum_{p prime} log(p)/p^6.

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

Offset

0,3

Comments

The negated first derivative of the prime zeta function at 6.

Links

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

R. J. Mathar, Series of reciprocal powers of k-almost primes arXiv:0803.0900, Table 3 s=6.

Eric Weisstein's MathWorld, Prime Zeta Function

Wikipedia, Prime Zeta Function

Example

0.012459080722799991527027792774689970040911350471575875874109334035...

Mathematica

RealDigits[PrimeZetaP'[6], 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: A104311 A200818 A021980 * A169624 A368797 A011175

Adjacent sequences: A303493 A303494 A303495 * A303497 A303498 A303499

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 25 2018

Status

approved