A341747 Decimal expansion of zeta(3) * zeta(4) * Product_{p prime} (1 + 1/p^2 - 2/p^3 - 2/p^5 + 2/p^6).

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

Offset

1,2

Comments

The constant c in the asymptotic formulas Sum_{n1, n2 <= x} sigma(lcm(n1, n2)) = c * x^4/4 + O(x^(7/2 + eps)) and Sum_{n1, n2 <= x} sigma(lcm(n1, n2))/(n1*n2) = c * x^2 + O(x^(3/2 + eps)).

Links

Table of n, a(n) for n=1..87.

Titus Hilberdink and László Tóth, On the average value of the least common multiple of k positive integers, Journal of Number Theory, Vol. 169 (2016), pp. 327-341. See p. 333.

Example

1.38692417041356586898814919766510683616526207826392...

Mathematica

$MaxExtraPrecision = 1500; m = 1500; c = LinearRecurrence[{0, -1, 2, 0, 2, -2}, {0, 2, -6, -2, 0, 2}, m]; Zeta[3] * Zeta[4] * Exp[NSum[Indexed[c, n]*PrimeZetaP[n]/n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]]

Prog

(PARI) zeta(3) * zeta(4) * prodeulerrat(1 + 1/p^2 - 2/p^3 - 2/p^5 + 2/p^6)

Crossrefs

Cf. A000203 (sigma), A240976, A341748.

Sequence in context: A152683 A154199 A083700 * A242672 A021725 A371472

Adjacent sequences: A341744 A341745 A341746 * A341748 A341749 A341750

Keyword

nonn,cons

Author

Amiram Eldar, Feb 18 2021

Status

approved