A038760 - OEIS

A038760

a(n) = n - floor(sqrt(n)) * ceiling(sqrt(n)).

0, 0, 0, 1, 0, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 3, 0, -3, -2, -1, 0, 1, 2, 3, 4, 0, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 0, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 0, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 0, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, -8, -7, -6, -5, -4

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,9

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = n - A000196(n)*A003059(n) = n - A038759(n).

EXAMPLE

Sqrt(31) is between 5 and 6, and 31 - 6*5 = 1, so a(31)=1.

MAPLE

a:= n-> n -(x-> floor(x)*ceil(x))(sqrt(n)):

seq(a(n), n=0..100); # Alois P. Heinz, Jan 03 2015