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

1, 7, 479, 413, 63397, 514639, 10410343, 1411432849, 6620481151, 6454614084953, 421950627598601, 8222379104323, 3989306589962303, 443539778381788333, 148124338024667050948691, 143366612154851808752629

Offset

3,2

Comments

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.

Links

Table of n, a(n) for n=3..18.

Formula

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

Example

A007406(n) begins 1, 5, 49, 205, 5269, 5369, 266681, 1077749, 9778141,..
a(3) = A007406( (5-1)/2 ) / 5 = 1
a(4) = A007406( (7-1)/2 ) / 7 = 49 / 7 = 7
a(5) = A007406( (11-1)/2 ) / 11 = 5269 / 11 = 479

Mathematica

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

Crossrefs

Cf. A007406.

Sequence in context: A261806 A332147 A278143 * A142734 A120773 A116167

Adjacent sequences: A119618 A119619 A119620 * A119622 A119623 A119624

Keyword

frac,nonn

Author

Alexander Adamchuk, Jun 07 2006

Status

approved