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A269404 Decimal expansion of Product_{k >= 1} (1 + 1/prime(k)^6). 0
1, 0, 1, 7, 0, 9, 2, 7, 6, 9, 1, 3, 0, 4, 9, 9, 2, 7, 6, 6, 4, 3, 2, 7, 2, 1, 3, 3, 0, 9, 7, 9, 0, 9, 9, 2, 0, 4, 9, 2, 2, 1, 9, 0, 7, 9, 4, 9, 4, 1, 0, 1, 1, 3, 4, 6, 6, 4, 6, 5, 1, 7, 9, 3, 8, 1, 8, 9, 3, 5, 3, 3, 5, 8, 3, 4, 2, 2, 7, 9, 4, 3, 1, 8, 1, 5, 1, 5, 9, 6, 4, 7, 8, 5, 0, 6, 6, 8, 9, 7, 8, 4, 5, 4, 6, 5, 1, 0, 6, 4, 0, 2, 6, 1, 3, 3, 6, 9, 3, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

More generally, Product_{k >= 1} (1 + 1/prime(k)^m) = Zeta(m)/Zeta(2*m), where Zeta(m) is the Riemann zeta function.

LINKS

Table of n, a(n) for n=1..120.

Eric Weisstein's World of Mathematics, Prime Products

FORMULA

Equals Zeta(6)/Zeta(12).

Equals 675675/(691*Pi^6).

EXAMPLE

1.0170927691304992766432721330979099204922190794941...

MATHEMATICA

RealDigits[Zeta[6]/Zeta[12], 10, 120][[1]]

RealDigits[675675/(691 Pi^6), 10, 120][[1]]

CROSSREFS

Cf. A082020, A157289, A157290, A157291.

Sequence in context: A198555 A234355 A021145 * A296433 A021589 A093444

Adjacent sequences:  A269401 A269402 A269403 * A269405 A269406 A269407

KEYWORD

nonn,cons

AUTHOR

Ilya Gutkovskiy, Feb 25 2016

STATUS

approved

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Last modified June 6 14:04 EDT 2020. Contains 334827 sequences. (Running on oeis4.)