A096625 Denominators of the Riemann prime counting function.

1, 1, 1, 2, 2, 2, 2, 6, 3, 3, 3, 3, 3, 3, 3, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60

Offset

1,4

Links

Table of n, a(n) for n=1..74.

Eric Weisstein's World of Mathematics, Riemann Prime Counting Function

Example

0, 1, 2, 5/2, 7/2, 7/2, 9/2, 29/6, 16/3, 16/3, 19/3, ...

Mathematica

Table[Sum[PrimePi[x^(1/k)]/k, {k, Log2[x]}], {x, 100}] // Denominator (* Eric W. Weisstein, Jan 09 2019 *)

Prog

(PARI) a(n) = denominator(sum(k=1, n, if (p=isprimepower(k), 1/p))); \\ Michel Marcus, Jan 07 2019
(PARI) a(n) = denominator(sum(k=1, logint(n, 2), primepi(sqrtnint(n, k))/k)); \\ Daniel Suteu, Jan 07 2019

Crossrefs

Cf. A096624.

Sequence in context: A119462 A293221 A334512 * A359072 A263455 A283677

Adjacent sequences: A096622 A096623 A096624 * A096626 A096627 A096628

Keyword

nonn,frac

Author

Eric W. Weisstein, Jul 01 2004

Status

approved