A067459 Sum of the remainders when n^2 is divided by squares less than n.

0, 0, 1, 7, 17, 15, 43, 58, 66, 90, 189, 211, 273, 336, 431, 398, 588, 689, 910, 872, 1199, 1435, 1438, 1862, 2007, 2079, 2208, 2764, 3329, 2964, 4356, 3945, 4359, 4633, 5330, 5855, 6210, 7491, 7821, 7406, 9610, 9373, 10309, 10606, 11965, 12362, 12468

Offset

1,4

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..n-1} (n^2 mod k^2). [From Robert Israel, Jan 07 2021 Maple program.]

Maple

f:= proc(n) local k; add(n^2 mod k^2, k=2..n-1) end proc:
map(f, [$1..100]); # Robert Israel, Jan 07 2021

Mathematica

Table[ Apply[ Plus, Mod[n^2, Table[i^2, {i, 1, n - 1} ]]], {n, 1, 50} ]

Prog

(PARI) a(n) = sum(k=1, n-1, n^2 % k^2); \\ Michel Marcus, Jan 09 2021

Crossrefs

Cf. A000290.

Sequence in context: A283163 A196164 A071615 * A323746 A101240 A191070

Adjacent sequences: A067456 A067457 A067458 * A067460 A067461 A067462

Keyword

easy,nonn

Author

Amarnath Murthy, Feb 07 2002

Extensions

Edited and extended by Robert G. Wilson v, Feb 08 2002

Status

approved