A067657 Prime values of A001008, the numerators of the harmonic numbers.

3, 11, 137, 761, 7129, 18858053, 34395742267, 85691034670497533, 252476961434436524654789, 928551009361054917576341971, 42409610330030873613929048033, 4868007055309996043055960217131137

Offset: 1

Author

Benoit Cloitre, Feb 03 2002

Keywords

• nonn

Comments

This sequence comprises the only primes for which 1/Sum_{k=1..c}(1/(a(n)*k)) is an integer for some c >= 2, yielding A002805(A056903(n)) for c = A056903(n). E.g. for n = 2: a(2) = 11, A056903(2) = 3, and 1 / (1/11 + 1/22 + 1/33) = 6 = A002805(A056903(2)). - Charles L. Hohn, Apr 02 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 1..43

Crossrefs

Cf. A001008, A056903.

Cf. A002805.

Programs

Mathematica

Table[ HarmonicNumber[n], {n, 0, 80}] // Numerator // Select[#, PrimeQ]& (* Jean-François Alcover, May 27 2013 *)

Formula

A001008 INTERSECT A000040.

a(n) = A001008(A056903(n)). - Amiram Eldar, Jun 02 2022