The Wolstenholme numbers are defined as the numerators of the generalized harmonic number  appearing in Wolstenholme's theorem. The first few are 1, 5, 49, 205, 5269, 5369, 266681, 1077749, ... (OEIS A007406).

By Wolstenholme's theorem,  for prime , where  is the th Wolstenholme number. In addition,  for prime .

The first few prime Wolstenholme numbers are 5, 266681, 40799043101, 86364397717734821, ... (OEIS A123751), which occur at indices , 7, 13, 19, 121, 188, 252, 368, 605, 745, ... (OEIS A111354).

REFERENCES:

Savio, D. Y.; Lamagna, E. A.; and Liu, S.-M. "Summation of Harmonic Numbers." In Computers and Mathematics (Ed. E. Kaltofen and S. M. Watt). New York: Springer-Verlag, pp. 12-20, 1989.

Sloane, N. J. A. Sequences A007406/M4004, A111354, and A123751 in "The On-Line Encyclopedia of Integer Sequences."