OFFSET
3,1
COMMENTS
The generalized harmonic number is H(n,m) = Sum_{k=1..n} 1/k^m. The numerator of the generalized harmonic number H(p-1,p) is divisible by p^3 for prime p>3. See A119722(n). The numerator of the generalized harmonic number H(p-1,p^2) is divisible by p^4 for prime p>3. In general, the numerator of the generalized harmonic number H(p-1,p^k) is divisible by p^(k+2) for prime p>3.
LINKS
Alexander Adamchuk, Jun 29 2007, Table of n, a(n) for n = 3..6
Eric Weisstein's World of Mathematics, Wolstenholme's Theorem
Eric Weisstein's World of Mathematics, Harmonic Number
FORMULA
a(n) = Numerator[ Sum[ 1/k^(Prime[n]^2), {k,1,Prime[n]-1} ] ] / Prime[n]^4 for n>2.
EXAMPLE
Prime[3] = 5.
a(3) = numerator[ 1 + 1/2^25 + 1/3^25 + 1/4^25 ] / 5^4 = 953962194872104906726451875/625 = 1526339511795367850762323.
MATHEMATICA
Table[ Numerator[ Sum[ 1/k^(Prime[n]^2), {k, 1, Prime[n]-1} ] ] / Prime[n]^4, {n, 3, 10} ]
CROSSREFS
KEYWORD
frac,nonn,uned,bref
AUTHOR
Alexander Adamchuk, Jun 29 2007
STATUS
approved