A176314 Sum of remainders of mod(n, k), for 1 <= k <= sqrt(n).

0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 3, 0, 2, 2, 1, 1, 4, 2, 5, 2, 2, 3, 6, 0, 3, 5, 6, 4, 8, 2, 6, 4, 5, 7, 6, 1, 6, 9, 11, 5, 10, 4, 9, 8, 5, 8, 13, 3, 8, 7, 10, 10, 16, 11, 12, 5, 8, 12, 18, 4, 10, 14, 10, 10, 12, 8, 15, 16, 20, 13, 20, 4, 11, 16, 15, 16, 16, 12, 19, 7, 11, 17, 25, 11, 14, 20, 25

Offset

1,11

Comments

It appears, as one would expect, that a(n) is asymptotically 1/4 n.

24 is the last n for which a(n) = 0.

Links

Table of n, a(n) for n=1..87.

Formula

a(n+1) = a(n) + floor(sqrt(n)) - A070039(n+1).

Mathematica

Total/@Table[Mod[n, k], {n, 90}, {k, Sqrt[n]}] (* Harvey P. Dale, Nov 20 2013 *)

Prog

(PARI) a(n) = sum(k=2, sqrtint(n), n%k)

Crossrefs

Cf. A004125, A070039.

Sequence in context: A331422 A279631 A102003 * A004587 A104609 A326395

Adjacent sequences: A176311 A176312 A176313 * A176315 A176316 A176317

Keyword

nonn

Author

Franklin T. Adams-Watters, Apr 15 2010

Status

approved