A229833 1/p^3 * numerator((sum_{j=1..p-1} j^(p-1)) - p*Bernoulli(p-1)) with p = prime(n).

17, 1175, 67232195, 1282936297603, 171594913930219489, 368517627392700495869, 259067037992493907740808871, 63098504840897942292160460526547792021, 4948605372033572359620687688871811178548595, 169413083241708480729625174442441002390094469490644564301, 90165569601996395473034926239938857618854516797194687641929891

Offset

3,1

Comments

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.

Links

Table of n, a(n) for n=3..13.

J. Sondow, Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771, in Proceedings of CANT 2011, arXiv:1110.3113

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.

Index entries for sequences related to Bernoulli numbers.

Example

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.

Mathematica

Table[p = Prime[n]; Numerator[ Sum[j^(p - 1), {j, 1, p - 1}] - p*BernoulliB[p - 1]]/p^3, {n, 3, 13}]

Crossrefs

Cf. A197630.

Sequence in context: A232942 A075602 A222985 * A362711 A305872 A172456

Adjacent sequences: A229830 A229831 A229832 * A229834 A229835 A229836

Keyword

nonn

Author

Jonathan Sondow, Oct 16 2013

Status

approved