A120290 Numerator of generalized harmonic number H(p-1,2p)= Sum[ 1/k^(2p), {k,1,p-1}] divided by p^2 for prime p>3.

2479157521, 159936660724017234488561, 1119583852472161859174156302552583713828739479026834819554843860744244189

Offset: 3

Author

Alexander Adamchuk, Jul 08 2006

Keywords

• frac
• nonn
• bref

Comments

Generalized harmonic number is H(n,m)= Sum[ 1/k^m, {k,1,n} ]. The numerator of generalized harmonic number H(p-1,2p) is divisible by p^2 for prime p>3.

Examples

			With prime(3) = 5, a(3) = numerator[ 1 + 1/2^10 + 1/3^10 + 1/4^10 ] / 5^2 = 61978938025 / 25 = 2479157521.
		

Links

• Alexander Adamchuk, First 5 terms.
• Eric Weisstein's World of Mathematics, Harmonic Number.
• Eric Weisstein's World of Mathematics, Wolstenholme's Theorem.

Crossrefs

Cf. A119722, A099828, A099827, A001008, A007406, A007408, A007410.

Programs

Mathematica

Table[Numerator[Sum[1/k^(2*Prime[n]),{k,1,Prime[n]-1}]],{n,3,7}]/Table[Prime[n]^2,{n,3,7}]

Formula

a(n) = numerator[ Sum[ 1/k^(2*Prime[n]), {k,1,Prime[n]-1} ]] / Prime[n]^2 for n>2.