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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 (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
Sequence in context: A166891 A184894 A111196 * A056918 A346671 A194471
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

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)