A382562 Decimal expansion of Sum_{p prime} 1/(p^2*(p + 1)).

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

Offset

0,2

Comments

The constant c in the formula Sum_{a,b <= x} omega(f(a,b)) = c * x^2 + O(x*log(x)^4), where omega = A001221, and f(a, b) = gcd(ab, a + b)/gcd(a, b) (Tóth, 2026, p. 4, Corollary 4). - Amiram Eldar, Jun 24 2026

Links

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

László Tóth, On the asymptotic density of the ordered pairs (a,b) of positive integers such that gcd(a*b,a+b) = gcd(a,b), arXiv:2606.20057 [math.NT], 2026. See p. 10 (Proof of Cor. 4).

Index to constants which are prime zeta sums {2,0,1}.

Formula

Equals A085548 - A179119.

Equals Sum_{k>=3} (-1)^(k+1) * P(k), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

Example

0.1220174937768622574914487767455031735289719237658219655861903295887428605710029...

Prog

(PARI) sumeulerrat(1/(p^2*(p+1))) \\ Amiram Eldar, Apr 01 2025

Crossrefs

Cf. A001221, A085548, A179119.

Sequence in context: A105929 A065600 A029583 * A011289 A288387 A225678

Adjacent sequences: A382559 A382560 A382561 * A382563 A382564 A382565

Keyword

nonn,cons,changed

Author

Artur Jasinski, Mar 31 2025

Status

approved