This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A229833 #16 May 16 2025 00:42:21
%S A229833 17,1175,67232195,1282936297603,171594913930219489,
%T A229833 368517627392700495869,259067037992493907740808871,
%U A229833 63098504840897942292160460526547792021,4948605372033572359620687688871811178548595,169413083241708480729625174442441002390094469490644564301,90165569601996395473034926239938857618854516797194687641929891
%N A229833 1/p^3 * numerator((sum_{j=1..p-1} j^(p-1)) - p*Bernoulli(p-1)) with p = prime(n).
%C A229833 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.
%H A229833 J. Sondow, <a href="http://arxiv.org/abs/1110.3113">Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771</a>, in Proceedings of CANT 2011, arXiv:1110.3113
%H A229833 J. Sondow, <a href="https://doi.org/10.1007/978-1-4939-1601-6_17">Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771</a>, Combinatorial and Additive Number Theory, CANT 2011 and 2012, Springer Proc. in Math. & Stat., vol. 101 (2014), pp. 243-255.
%H A229833 <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>
%e A229833 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.
%t A229833 Table[p = Prime[n]; Numerator[ Sum[j^(p - 1), {j, 1, p - 1}] - p*BernoulliB[p - 1]]/p^3, {n, 3, 13}]
%Y A229833 Cf. A197630.
%K A229833 nonn
%O A229833 3,1
%A A229833 _Jonathan Sondow_, Oct 16 2013