A394336 Decimal expansion of Product_{p prime} (1 + 1/(p^6 - p^4)).

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

Offset

1,3

Comments

The asymptotic mean of the number of cubefull divisors of the greatest common divisor of two positive integers selected independently at random.

In general, the asymptotic mean of the number of k-full divisors (k-full numbers are numbers whose prime factorization has no exponent that is smaller than k) of the greatest common divisor of two positive integers selected independently at random is Product_{p prime} (1 + 1/(p^(2*k) - p^(2*k-2))).

Links

Table of n, a(n) for n=1..105.

Formula

Equals lim_{m->oo} (1/m^2) * Sum_{i,j=1..m} A190867(gcd(i, j)).

Equals zeta(2) * Product_{p prime} (1- 1/p^2 + 1/p^6) = A013661 * A393649.

Example

1.022486596136980366191611409373598359445927292726914...

Prog

(PARI) prodeulerrat(1 + 1/(p^6 - p^4))

Crossrefs

Cf. A013661, A036966, A190867, A393649, A394335.

Sequence in context: A123958 A377231 A048572 * A337561 A121173 A388154

Adjacent sequences: A394333 A394334 A394335 * A394337 A394338 A394339

Keyword

nonn,cons

Author

Amiram Eldar, Mar 17 2026

Status

approved