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%I #5 Jan 04 2013 11:54:26
%S 2063,2743174627,19563315706517008974432827112201617,
%T 2597378078067393746941400113704449589199274012223316613,
%U 777478358612529699991463948563778410644748121498526065585976638854277886379480749840301120148933
%N Numerator of generalized harmonic number H(p-1,p)= Sum[ 1/k^p, {k,1,p-1}] divided by p^3 for prime p>3.
%C Generalized harmonic number is H(n,m)= Sum[ 1/k^m, {k,1,n} ]. The numerator of generalized harmonic number H(p-1,p) is divisible by p^3 for prime p>3.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WolstenholmesTheorem.html">Wolstenholme's Theorem</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%F a(n) = numerator[ Sum[ 1/k^Prime[n], {k,1,Prime[n]-1} ]] / Prime[n]^3 for n>2.
%e Prime[3] = 5.
%e a(3) = numerator[ 1 + 1/2^5 + 1/3^5 + 1/4^5 ] / 5^3 = 257875/125 = 2063.
%e Prime[4] = 7
%e a(4) = numerator[ 1 + 1/2^7 + 1/3^7 + 1/4^7 + 1/5^7 + 1/6^7 ] / 7^3 = 2743174627.
%t Numerator[Table[Sum[1/k^Prime[n],{k,1,Prime[n]-1}],{n,3,9}]]/Table[Prime[n]^3,{n,3,9}]
%Y Cf. A099828, A099827, A001008, A007406, A007408, A007410.
%K frac,nonn
%O 3,1
%A _Alexander Adamchuk_, Jun 13 2006
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