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.

A229211 Numbers k such that Sum_{j=1..k} (j*(j+1)/2 - sigma(j))^j == 0 (mod k), where sigma(j) = A000203(j) and j*(j+1)/2 - sigma(j) = A024816(j).

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%I A229211 #20 Apr 20 2022 09:38:45
%S A229211 1,2,9,78,3205,5589,14153,246123
%N A229211 Numbers k such that Sum_{j=1..k} (j*(j+1)/2 - sigma(j))^j == 0 (mod k), where sigma(j) = A000203(j) and j*(j+1)/2 - sigma(j) = A024816(j).
%C A229211 Tested up to k = 50000.
%e A229211 (1*2 / 2 - sigma(1))^1 + (2*3 / 2 - sigma(2))^2 + ... + (9*10 / 2 - sigma(10))^9 = 35223475538772 and 35223475538772 / 9 = 3913719504308.
%p A229211 with(numtheory); P:=proc(q) local n, t; t:=0;
%p A229211 for n from 1 to q do t:=t+(n*(n+1)/2-sigma(n))^n; if t mod n=0 then print(n); fi; od; end: P(10^6);
%o A229211 (PARI) isok(n) = sum(i=1, n, (i*(i+1)/2 - sigma(i))^i) % n == 0; \\ _Michel Marcus_, Nov 09 2014
%Y A229211 Cf. A000203, A227427, A227429, A227502, A227848, A229095, A229207-A229210.
%K A229211 nonn,more
%O A229211 1,2
%A A229211 _Paolo P. Lava_, Sep 16 2013
%E A229211 Typo in name and crossref corrected by _Michel Marcus_, Nov 09 2014
%E A229211 a(8) from _Kevin P. Thompson_, Apr 20 2022