A341748 Decimal expansion of zeta(3) * Product_{p prime} (1 - 3/p^2 + 2/p^3 - 1/p^4 + 2/p^5 - 1/p^6).

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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..86.

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

0.33091829620850886597708997991322785489354334541048...

Mathematica

$MaxExtraPrecision = 1500; m = 1500; c = LinearRecurrence[{-1, 2, 0, 1, -1}, {0, -6, 6, -22, 40}, m]; f[x_] := 1 - 3 x^2 + 2 x^3 - x^4 + 2 x^5 - x^6; Zeta[3] * f[1/2] * f[1/3] * Exp[NSum[Indexed[c, n]*(PrimeZetaP[n] - 1/2^n - 1/3^n)/n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]]

Prog

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

Crossrefs

Cf. A000010 (phi), A240976, A341747.

Sequence in context: A275408 A169670 A372004 * A120981 A298850 A262292

Adjacent sequences: A341745 A341746 A341747 * A341749 A341750 A341751

Keyword

nonn,cons

Author

Amiram Eldar, Feb 18 2021

Status

approved