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 A226965 #26 Sep 06 2018 10:10:13
%S A226965 1,2,6,7,14,294,12642
%N A226965 Numbers n such that 1^n + 2^n + 3^n +...+ n^n == 7 (mod n).
%C A226965 Also, integers n such that B(n)*n == 7 (mod n), where B(n) is the n-th Bernoulli number, or SUM[prime p, (p-1) divides n] n/p == -7 (mod n). It is easy to see that for n>1, every prime divisor p of n, except p=7, must appear in first power, while p=7 may appear in first or second power. Moreover, the multiset P of prime divisors of all such n satisfies the property: if p is in P, then p-1 is the product of distinct elements of P. This multiset is P = {2, 3, 7, 7, 43}, implying that the sequence is finite and complete. - _Max Alekseyev_, Aug 25 2013
%H A226965 M. A. Alekseyev, J. M. Grau, A. M. Oller-Marcen. Computing solutions to the congruence 1^n + 2^n + ... + n^n == p (mod n). Discrete Applied Mathematics, 2018. doi:<a href="http://doi.org/10.1016/j.dam.2018.05.022">10.1016/j.dam.2018.05.022</a> arXiv:<a href="http://arxiv.org/abs/1602.02407">1602.02407</a> [math.NT]
%t A226965 Select[Range[10000], Mod[Sum[PowerMod[i, #, #], {i, #}], #] == 7&]
%o A226965 (PARI) is(n)=Mod(sumdiv(n, d, if(isprime(d+1), n/(d+1))), n)==-7 \\ _Charles R Greathouse IV_, Nov 13 2013
%Y A226965 Cf. A031971.
%Y A226965 Solutions to 1^n+2^n+...+n^n == m (mod n): A005408 (m=0), A014117 (m=1), A226960 (m=2), A226961 (m=3), A226962(m=4), A226963 (m=5), A226964 (m=6), this sequence (m=7), A226966 (m=8), A226967 (m=9), A280041 (m=19), A280043 (m=43), A302343 (m=79), A302344 (m=193).
%K A226965 nonn,full,fini
%O A226965 1,2
%A A226965 _José María Grau Ribas_, Jun 24 2013
%E A226965 Corrected and keywords full,fini added by _Max Alekseyev_, Aug 25 2013