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Search: id:A134296
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| A134296 |
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Quotients A134295(p)/p = Sum[ (p-k)!*(k-1)! - (-1)^k), {k,1,p} ]/p, where p = Prime[n]. |
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2
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| 1, 2, 13, 259, 750371, 81566917, 2642791002353, 716984262871579, 102688143363690674087, 21841112114495269555043222069, 17727866746681961093761724283871
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OFFSET
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1,2
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COMMENT
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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, ...}.
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FORMULA
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a(n) = Sum[ (Prime[n]-k)!*(k-1)! - (-1)^k, {k,1,Prime[n]} ] / Prime[n].
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MATHEMATICA
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Table[ (Sum[ (Prime[n]-k)!*(k-1)! - (-1)^k, {k, 1, Prime[n]} ]) / Prime[n], {n, 1, 20} ]
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CROSSREFS
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Cf. A007540, A007619 = Wilson quotients:((p-1)!+1)/p. Cf. A134295 = Sum[ (n-k)!*(k-1)! - (-1)^k, {k, 1, n} ].
Sequence in context: A135870 A133067 A042677 this_sequence A086510 A123113 A126742
Adjacent sequences: A134293 A134294 A134295 this_sequence A134297 A134298 A134299
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 17 2007
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