A072516 Sum of remainders when n is divided by lesser squares.

0, 0, 0, 0, 1, 2, 3, 0, 1, 3, 5, 3, 5, 7, 9, 7, 10, 4, 7, 6, 9, 12, 15, 14, 17, 21, 16, 16, 20, 24, 28, 12, 16, 20, 24, 15, 20, 25, 30, 31, 36, 41, 46, 47, 43, 48, 53, 38, 43, 24, 30, 32, 38, 35, 41, 43, 49, 55, 61, 63, 69, 75, 72, 58, 65, 72, 79, 82, 89, 96, 103, 61, 68, 75, 57, 60

Offset

1,6

Links

Table of n, a(n) for n=1..76.

Example

a(25) = 17. The squares < 25 are 4, 9 and 16 and the remainders are 1, 7 and 9 and the sum = 17.

Mathematica

a[n_] := Sum[Mod[n, k^2], {k, 1, Floor[Sqrt[n]]}]
Table[Total[Table[Mod[k, n], {n, Range[Floor[Sqrt[k]]]^2}]], {k, 80}] (* Harvey P. Dale, Jan 04 2024 *)

Crossrefs

Sequence in context: A089652 A195467 A112168 * A320782 A191588 A106450

Adjacent sequences: A072513 A072514 A072515 * A072517 A072518 A072519

Keyword

nonn

Author

Amarnath Murthy, Jul 31 2002

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 25 2003 and Dean Hickerson, Apr 28 2003

Status

approved