A394427 Decimal expansion of Product_{p prime} ((1-1/p)^2 * Sum_{k>=0} (k^2+1)/p^(k^2)).

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

Offset

0,1

Comments

The asymptotic probability that the product of two positive integers selected independently at random is a number whose prime factorization exponents are all squares (A197680).

Links

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

Example

0.349622561337888279499195419864524551535567669131557...

Prog

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

Crossrefs

Cf. A197680, A394428.

Similar constants: A394004, A394008, A394011.

Sequence in context: A023183 A102320 A227717 * A021290 A016656 A319021

Adjacent sequences: A394424 A394425 A394426 * A394428 A394430 A394431

Keyword

nonn,cons

Author

Amiram Eldar, Mar 20 2026

Status

approved