A398529 - OEIS

A398529

Decimal expansion of Sum_{k>=1} omega(k)/(k*(k+1)), where omega(k) = A001221(k) is the number of distinct primes dividing k.

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

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OFFSET

0,1

COMMENTS

This constant appears in the asymptotic formula for A398528.

LINKS

Table of n, a(n) for n=0..104.

Olivier Bordellès, On certain sums of number theory, International Journal of Number Theory, Vol. 18, No. 9 (2022), pp. 2053-2074; arXiv preprint, arXiv:2009.05751 [math.NT], 2020.

Mihoub Bouderbala and Meselem Karras, On a sum involving the number of distinct prime factors function related to the integer part function, Notes on Number Theory and Discrete Mathematics, Vol. 26, No. 4 (2020), pp. 52-56.

Kui Liu, Jie Wu, and Zhishan Yang, On some sums involving the integral part function, International Journal of Number Theory, Vol. 20, No. 3 (2024), pp. 831-847; arXiv preprint, arXiv:2109.01382 [math.NT], 2021.

FORMULA

Equals Sum_{k>=2} (-1)^k * D(k), where D(s) = zeta(s) * prime_zeta(s) is the Dirichlet g.f. of omega.

EXAMPLE

0.591845878310049824648351814607086786452855786471936...

PROG

(PARI) suminf(k = 2, (-1)^k * zeta(k) * sumeulerrat(1/p, k))

CROSSREFS

Cf. A001221, A398528.

Sequence in context: A266553 A306980 A063921 * A346044 A334402 A227574

Adjacent sequences: A398526 A398527 A398528 * A398530 A398531 A398532

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Aug 01 2026

STATUS

approved