A309341 a(n) = Sum_{j=1..n*(n-1)} (n*j mod (n+j)).

0, 2, 19, 67, 185, 373, 742, 1249, 2053, 3111, 4672, 6467, 9113, 12164, 16124, 20862, 26801, 33376, 41889, 51089, 62342, 75007, 89949, 106152, 125610, 146699, 170757, 197305, 227912, 259643, 297469, 336895, 381304, 429869, 483295, 539575, 603725, 670931, 745068, 823421, 910928

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

Sequence in context: A218547 A365494 A232537 * A079773 A217082 A024220

Adjacent sequences: A309338 A309339 A309340 * A309342 A309343 A309344

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 24 2019

Status

approved