A338589 Sum of the remainders (s*t mod n), where s + t = n and 1 <= s <= t.

0, 1, 2, 3, 5, 10, 14, 18, 15, 25, 33, 41, 39, 56, 70, 68, 68, 75, 95, 115, 119, 132, 161, 190, 125, 169, 180, 217, 203, 260, 279, 296, 286, 289, 350, 339, 333, 380, 455, 490, 410, 469, 473, 561, 525, 598, 658, 716, 539, 575, 697, 715, 689, 738, 880, 966, 836, 841, 944, 1105, 915

Offset

1,3

Links

Table of n, a(n) for n=1..61.

Formula

a(n) = Sum_{i=1..floor(n/2)} ( i*(n-i) mod n ).

Example

a(6) = 10; ((1*5) mod 6) + ((2*4) mod 6) + ((3*3) mod 6) = 5 + 2 + 3 = 10.

Mathematica

Table[Sum[Mod[i (n - i), n], {i, Floor[n/2]}], {n, 80}]

Crossrefs

Sequence in context: A120610 A090859 A004681 * A222406 A044953 A297130

Adjacent sequences: A338586 A338587 A338588 * A338590 A338591 A338592

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 07 2020

Status

approved