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A134296 Quotients A134295(p)/p = Sum[ (p-k)!*(k-1)! - (-1)^k), {k,1,p} ]/p, where p = Prime[n]. 1
1, 2, 13, 259, 750371, 81566917, 2642791002353, 716984262871579, 102688143363690674087, 21841112114495269555043222069, 17727866746681961093761724283871 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A134295(n) = Sum[ (n-k)!*(k-1)! - (-1)^k, {k, 1, n} ] = {2, 2, 6, 16, 65, 312, 1813, 12288, 95617, 840960, 8254081, ...}. According to the Generalized Wilson-Lagrange Theorem a prime p divides (p-k)!*(k-1)! - (-1)^k for all integer k>0. a(n) = A134295(p)/p for p = Prime[n]. a(n) is prime for n = {2, 3, 7, 9, 37, ...}. Corresponding prime terms in a(n) are {2, 13, 2642791002353, 102688143363690674087, ...}.

LINKS

Table of n, a(n) for n=1..11.

FORMULA

a(n) = Sum[ (Prime[n]-k)!*(k-1)! - (-1)^k, {k,1,Prime[n]} ] / Prime[n].

MATHEMATICA

Table[ (Sum[ (Prime[n]-k)!*(k-1)! - (-1)^k, {k, 1, Prime[n]} ]) / Prime[n], {n, 1, 20} ]

CROSSREFS

Cf. A007540, A007619 = Wilson quotients:((p-1)!+1)/p. Cf. A134295 = Sum[ (n-k)!*(k-1)! - (-1)^k, {k, 1, n} ].

Sequence in context: A133067 A276744 A042677 * A086510 A326360 A123113

Adjacent sequences:  A134293 A134294 A134295 * A134297 A134298 A134299

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Oct 17 2007

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)