A106830 Numerator of Sum_{ primes p <= n} 1/p.

0, 1, 5, 5, 31, 31, 247, 247, 247, 247, 2927, 2927, 40361, 40361, 40361, 40361, 716167, 716167, 14117683, 14117683, 14117683, 14117683, 334406399, 334406399, 334406399, 334406399, 334406399, 334406399, 9920878441, 9920878441, 314016924901, 314016924901

Offset

1,3

Comments

Very similar to A024451, which see for further information.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

0, 1/2, 5/6, 5/6, 31/30, 31/30, 247/210, 247/210, 247/210, 247/210, 2927/2310, 2927/2310, 40361/30030, 40361/30030, 40361/30030, ...

Mathematica

Accumulate[Table[If[PrimeQ[n], 1/n, 0], {n, 40}]]//Numerator (* Harvey P. Dale, Feb 17 2018 *)

Crossrefs

Denominators are in A034386.

The following fractions are all related to each other: Sum 1/n: A001008/A002805, Sum 1/prime(n): A024451/A002110 and A106830/A034386, Sum 1/nonprime(n): A282511/A282512, Sum 1/composite(n): A250133/A296358.

Sequence in context: A117858 A365824 A014434 * A265798 A259264 A259265

Adjacent sequences: A106827 A106828 A106829 * A106831 A106832 A106833

Keyword

nonn,frac

Author

N. J. A. Sloane, May 22 2005

Status

approved