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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. 3
2479157521, 159936660724017234488561, 1119583852472161859174156302552583713828739479026834819554843860744244189 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

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.

LINKS

Alexander Adamchuk, First 5 terms

Eric Weisstein's World of Mathematics, Wolstenholme's Theorem.

Eric Weisstein's World of Mathematics, harmonic number.

FORMULA

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

EXAMPLE

Prime[3] = 5.

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

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A131013 A289544 A258611 * A308377 A271105 A134439

Adjacent sequences:  A120287 A120288 A120289 * A120291 A120292 A120293

KEYWORD

frac,nonn,bref

AUTHOR

Alexander Adamchuk, Jul 08 2006

STATUS

approved

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Last modified October 27 13:40 EDT 2021. Contains 348276 sequences. (Running on oeis4.)