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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, Harmonic Number.
Eric Weisstein's World of Mathematics, Wolstenholme's Theorem.
FORMULA
a(n) = numerator[ Sum[ 1/k^(2*Prime[n]), {k,1,Prime[n]-1} ]] / Prime[n]^2 for n>2.
EXAMPLE
With 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
Sequence in context: A131013 A289544 A258611 * A308377 A271105 A134439
KEYWORD
frac,nonn,bref
AUTHOR
Alexander Adamchuk, Jul 08 2006
STATUS
approved

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Last modified April 24 08:59 EDT 2024. Contains 371935 sequences. (Running on oeis4.)