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A119621 Wolstenholme numbers A007406 ( numerator of Sum 1/k^2, k = 1..(p-1)/2 ) divided by prime p>3. 0

%I #2 Mar 31 2012 13:20:26

%S 1,7,479,413,63397,514639,10410343,1411432849,6620481151,

%T 6454614084953,421950627598601,8222379104323,3989306589962303,

%U 443539778381788333,148124338024667050948691,143366612154851808752629

%N Wolstenholme numbers A007406 ( numerator of Sum 1/k^2, k = 1..(p-1)/2 ) divided by prime p>3.

%C Wolstenholme numbers A007406(n) (numerator of Sum 1/k^2, k = 1..n) are divisible by prime p > 3 for n = (p-1)/2. a(n) = A007406((p-1)/2) / p, where p = Prime[n] > 3.

%F a(n) = numerator[ Sum[ 1/i^2, {i,1,(Prime[n]-1)/2} ] ] / Prime[n] for n > 3.

%e A007406(n) begins 1, 5, 49, 205, 5269, 5369, 266681, 1077749, 9778141,..

%e a(3) = A007406( (5-1)/2 ) / 5 = 1

%e a(4) = A007406( (7-1)/2 ) / 7 = 49 / 7 = 7

%e a(5) = A007406( (11-1)/2 ) / 11 = 5269 / 11 = 479

%t Table[Numerator[Sum[1/i^2,{i,1,(Prime[n]-1)/2}]]/Prime[n],{n,3,25}]

%Y Cf. A007406.

%K frac,nonn

%O 3,2

%A _Alexander Adamchuk_, Jun 07 2006

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