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).
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."
appearing in Wolstenholme's theorem. The
first few are 1, 5, 49, 205, 5269, 5369, 266681, 1077749, ... (OEIS A007406).
for prime 
, where 
is the 
th Wolstenholme number. In addition, 
for prime 
.
,
7, 13, 19, 121, 188, 252, 368, 605, 745, ... (OEIS A111354).
