A394041 - OEIS

A394041

Decimal expansion of Product_{p prime} (1 - 1/(1 + p + p^2)^2).

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

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OFFSET

0,1

COMMENTS

The asymptotic probability that the greatest common divisor of two cubefree numbers (A004709) selected independently at random is a squarefree number (A005117).

LINKS

Table of n, a(n) for n=0..105.

FORMULA

Equals zeta(3)^2 * A394042.

Equals (zeta(3)^2/zeta(2)) * Product_{p prime} (1 + 1/p^2 - 2/p^3) = A183030 * A059956 * A330594.

EXAMPLE

0.972374431435158684101789348678887545288026724358652...

PROG

(PARI) prodeulerrat(1 - 1/(1 + p + p^2)^2)

CROSSREFS

Cf. A002117, A004709, A005117, A059956, A183030, A330594, A394042, A394043.

Sequence in context: A328968 A267316 A346907 * A021511 A029688 A155792

Adjacent sequences: A394037 A394039 A394040 * A394042 A394043 A394044

KEYWORD

nonn,cons

AUTHOR

Amiram Eldar, Mar 08 2026

STATUS

approved