A393951 Decimal expansion of Sum_{p prime, k>=0} 1/(p^(2^(k+1)) + 2*p^(2^k)) * Product_{p prime} ((1-1/p)^2 * Product_{k>=0} (1 + 2/p^(2^k))).

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

Offset

0,1

Comments

The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is a "Fermi-Dirac prime" (A050376).

Links

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

Formula

Equals Sum_{p prime, k>=0} 1/(p^(2^(k+1)) + 2*p^(2^k)) * A393948.

Example

0.235439084951993028533217989556236772680136440488478...

Prog

(PARI) c(m) = sumeulerrat(sum(k = 0, m, 1/(p^(2^(k+1)) + 2*p^(2^k)))) * prodeulerrat((1 - 1/p)^2 * prod(k = 0, m, 1 + 2/p^(2^k)));
{my(c1 = 0, c2 = 1, m = 1); while(c2 != c1, c1 = c2; c2 = c(m); m++); c2}

Crossrefs

Cf. A050376, A077609.

The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is: A065472 (square), A393948 (1), A393949 (prime), A393950 (squarefree), this constant (Fermi-Dirac prime), A393952 (exponentially 2^n-number), A393953 (4th power).

Sequence in context: A123274 A214674 A185332 * A023818 A102149 A321782

Adjacent sequences: A393948 A393949 A393950 * A393952 A393953 A393954

Keyword

nonn,cons

Author

Amiram Eldar, Mar 04 2026

Status

approved