A236436 Denominator of product_{k=1..n-1} (1 + 1/prime(k)).

1, 2, 1, 5, 35, 385, 715, 12155, 46189, 1062347, 30808063, 955049953, 1859834119, 76253198879, 298080686527, 14009792266769, 742518990138757, 43808620418186663, 86204059532560853, 339745411098916303, 24121924188023057513, 47591904479072518877, 3759760453846728991283

Offset

1,2

References

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979; Theorem 429.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

J. Sondow and E. Weisstein, MathWorld: Mertens Theorem

Formula

A236435(n+1) / a(n+1) = A072045(n)/A072044(n) / A038110(n+1)/A060753(n+1) because 1+x = (1-x^2) / (1-x).

A236436(n) / a(n) = product_{k=1..n-1} (1 + 1/prime(k)) ~ (6/Pi^2)*exp(gamma)*log(n) as n -> infinity, by Mertens' theorem.

Example

(1 + 1/2)*(1 + 1/3)*(1 + 1/5)*(1 + 1/7) = 96/35 has denominator a(5) = 35.

Mathematica

Denominator@Table[Product[1 + 1/Prime[k], {k, 1, n - 1}], {n, 1, 23}]

Crossrefs

Cf. A038110, A060753, A072044, A072045, A236435.

Sequence in context: A370163 A075403 A260503 * A187618 A320101 A343018

Adjacent sequences: A236433 A236434 A236435 * A236437 A236438 A236439

Keyword

nonn,frac

Author

Jonathan Sondow, Feb 01 2014

Status

approved