A394011 Decimal expansion of Product_{p prime} (1-1/p)^2 * (1 + Sum_{k >= 0} (2^k + 1)/p^(2^k)).

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

Offset

0,1

Comments

The asymptotic probability that the product of two positive integers selected independently at random is an exponentially 2^n number (A138302).

Links

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

Example

0.683988141437805930435510053776353193243930422806695...

Prog

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

Crossrefs

Cf. A138302, A065473 (squarefree analog), A394004 (exponentially odd analog), A394008 (cubefree analog).

Sequence in context: A054042 A184084 A346402 * A255728 A272488 A396438

Adjacent sequences: A394008 A394009 A394010 * A394012 A394013 A394014

Keyword

nonn,cons

Author

Amiram Eldar, Mar 06 2026

Status

approved