A229211 - OEIS

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).

1, 2, 9, 78, 3205, 5589, 14153, 246123

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Tested up to k = 50000.

LINKS

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

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

Typo in name and crossref corrected by Michel Marcus, Nov 09 2014

a(8) from Kevin P. Thompson, Apr 20 2022

STATUS

approved