cp's OEIS Frontend

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.

A229208 Numbers k such that Sum_{j=1..k} sigma(j)^j == 0 (mod k).

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%I A229208 #24 Feb 14 2021 08:12:56
%S A229208 1,2,9,55,758,16685,29224,84293,87018,98122
%N A229208 Numbers k such that Sum_{j=1..k} sigma(j)^j == 0 (mod k).
%C A229208 a(8) > 50000.
%C A229208 a(11) > 10^5. - _Hiroaki Yamanouchi_, Sep 23 2014
%e A229208 sigma(1)^1 + sigma(2)^2 + ... + sigma(9)^9 = 13172483385 and 13172483385 / 9 = 1463609265.
%p A229208 with(numtheory); P:=proc(q) local n, t; t:=0;
%p A229208 for n from 1 to q do t:=t+sigma(n)^n; if t mod n=0 then print(n);
%p A229208 fi; od; end: P(10^6);
%t A229208 Module[{nn=100000},Select[Thread[{Accumulate[Table[DivisorSigma[1,n]^n,{n,nn}]],Range[nn]}],Divisible[#[[1]],#[[2]]]&]][[All,2]] (* _Harvey P. Dale_, Dec 06 2018 *)
%o A229208 (PARI) lista(nn) = {v = vector(nn, i, sigma(i)); for (n=1, nn, if (! sum(i=1, n, Mod(v[i], n)^i), print1(n, ", ");););} \\ _Michel Marcus_, Sep 21 2013
%Y A229208 Cf. A000203, A227427, A227429, A227502, A227848, A229095, A229207, A229209-A229211.
%K A229208 nonn,more
%O A229208 1,2
%A A229208 _Paolo P. Lava_, Sep 16 2013
%E A229208 a(8)-a(10) from _Hiroaki Yamanouchi_, Sep 23 2014