OFFSET
1,2
COMMENTS
Sum goes up to j = n*(n-1) because n*j == j-n*(n-1) (mod (n+j)) for j >= n*(n-1).
LINKS
Robert Israel, Table of n, a(n) for n = 1..2000
Robert Israel, Plot of a(n)/n^4 for 100 <= n <= 2000
FORMULA
Conjecture: a(n) ~ c*n^4 where c = 0.32246....
EXAMPLE
For k = 3, 1*3 = 3 == 3 (mod 4), 2*3 = 6 == 1 (mod 5), 3*3 = 9 == 3 (mod 6), 4*3 = 12 == 5 (mod 7), 5*3=15 == 7 (mod 8), 6*3 = 18 == 0 (mod 9), so a(3) = 3+1+3+5+7 = 19.
MAPLE
f:= k -> add((k*j) mod (k+j), j=1..k*(k-1)-1):
map(f, [$1..30]);
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jul 24 2019
STATUS
approved