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URL: https://oeis.org/A229211

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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).
5
1, 2, 9, 78, 3205, 5589, 14153, 246123
OFFSET
1,2
COMMENTS
Tested up to k = 50000.
EXAMPLE
(1*2 / 2 - sigma(1))^1 + (2*3 / 2 - sigma(2))^2 + ... + (9*10 / 2 - sigma(10))^9 = 35223475538772 and 35223475538772 / 9 = 3913719504308.
MAPLE
with(numtheory); P:=proc(q) local n, t; t:=0;
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);
PROG
(PARI) isok(n) = sum(i=1, n, (i*(i+1)/2 - sigma(i))^i) % n == 0; \\ Michel Marcus, Nov 09 2014
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Sep 16 2013
EXTENSIONS
Typo in name and crossref corrected by Michel Marcus, Nov 09 2014
a(8) from Kevin P. Thompson, Apr 20 2022
STATUS
approved