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A034602
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Wolstenholme quotient W_p = (binomial(2p-1,p) - 1)/p^3 for prime p=A000040(n).
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18
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1, 5, 265, 2367, 237493, 2576561, 338350897, 616410400171, 7811559753873, 17236200860123055, 3081677433937346539, 41741941495866750557, 7829195555633964779233, 21066131970056662377432067
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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COMMENTS
| Equivalently, (binomial(2p,p)-2)/(2*p^3) where p runs through the primes >=5.
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, Sect. B31.
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LINKS
| McIntosh, R. J. (1995), On the converse of Wolstenholme's theorem, Acta Arithmetica 71 (4): 381-389.
R. Mestrovic, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv:1111.3057, 2011
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FORMULA
| a(n) = (A088218(p)-1)/p^3 = (A001700(p-1)-1)/p^3 = (A000984(p)-2)/(2*p^3), where p=A000040(n).
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EXAMPLE
| Binomial(10,5)-2 = 250; 5^3=125 hence a(5)=1
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CROSSREFS
| Cf. A177783 (alternative definition of Wolstenholme quotient), A072984, A092101, A092103, A092193, A128673.
Sequence in context: A159954 A079681 A086656 * A175180 A113257 A180820
Adjacent sequences: A034599 A034600 A034601 * A034603 A034604 A034605
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by Max Alekseyev (maxale(AT)gmail.com), May 14 2010
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