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A229833
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1/p^3 * numerator((sum_{j=1..p-1} j^(p-1)) - p*Bernoulli(p-1)) with p = prime(n).
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0
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17, 1175, 67232195, 1282936297603, 171594913930219489, 368517627392700495869, 259067037992493907740808871, 63098504840897942292160460526547792021, 4948605372033572359620687688871811178548595, 169413083241708480729625174442441002390094469490644564301, 90165569601996395473034926239938857618854516797194687641929891
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OFFSET
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3,1
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COMMENTS
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Sum_{j=1..p-1} j^(p-1)) == p*Bernoulli(p-1) (mod p^3) for prime p > 3 (see formulas (8) and (10) in "Lerch Quotients, ..."), so a(n) is an integer for n > 2.
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LINKS
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J. Sondow, Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771, Combinatorial and Additive Number Theory, CANT 2011 and 2012, Springer Proc. in Math. & Stat., vol. 101 (2014), pp. 243-255.
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EXAMPLE
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Prime(3) = 5 and 1/5^3 * numerator((sum_{j=1..4} j^4) - 5*Bernoulli(4)) = 1/125 * numerator(354 - 5*(-1/6)) = 2125/125 = 17, so a(3) = 17.
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MATHEMATICA
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Table[p = Prime[n]; Numerator[ Sum[j^(p - 1), {j, 1, p - 1}] - p*BernoulliB[p - 1]]/p^3, {n, 3, 13}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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