A393293 - OEIS

A393293

Decimal expansion of Product_{p prime} (1 - (p-1)^3/(p^3*(p^3-1))).

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

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OFFSET

0,1

COMMENTS

The asymptotic probability that the greatest common unitary divisor of three positive integers selected independently at random equals 1 (Tóth, 2014).

In general, the asymptotic probability that the greatest common unitary divisor of k positive integers selected independently at random equals 1 is Product_{p prime} (1 - (p-1)^k/(p^k*(p^k-1))).

LINKS

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

László Tóth, Multiplicative arithmetic functions of several variables: a survey, in: T. Rassias and P. Pardalos (eds.), Mathematics Without Boundaries: Surveys in Pure Mathematics, New York, NY: Springer New York, 2014, pp. 483-514; arXiv preprint, arXiv:1310.7053 [math.NT], 2013-2014. See Proposition 22, p. 507.

FORMULA

Equals zeta(3) * Product_{p prime} (1 - 2/p^3 + 3/p^4 - 3/p^5 + 1/p^6).

EXAMPLE

0.963764081460077154108621545444533216762123221644108...

PROG

(PARI) prodeulerrat(1 - (p-1)^3/(p^3*(p^3-1)))

CROSSREFS

Cf. A002117, A077610, A306071, A319593.

Sequence in context: A226582 A276538 A243313 * A259469 A241993 A099817

Adjacent sequences: A393290 A393291 A393292 * A393294 A393295 A393296

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Mar 10 2026

STATUS

approved