A132295 Sum of the nonsquare numbers not larger than n.

0, 2, 5, 5, 10, 16, 23, 31, 31, 41, 52, 64, 77, 91, 106, 106, 123, 141, 160, 180, 201, 223, 246, 270, 270, 296, 323, 351, 380, 410, 441, 473, 506, 540, 575, 575, 612, 650, 689, 729, 770, 812, 855, 899, 944, 990, 1037, 1085, 1085, 1135, 1186, 1238, 1291, 1345

Offset: 1

Author

Cino Hilliard, Nov 07 2007

Keywords

• nonn
• easy

Examples

			Let n=5. The sum of the nonsquare numbers <= 5 is 2+3+5 = 10, the 5th entry in the sequence.
		

Links

• Jason Yuen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000037, A000330, A086849.

Programs

Mathematica

Table[Total[Select[Range[n],!IntegerQ[Sqrt[#]]&]],{n,54}] (* James C. McMahon, Mar 04 2025 *)

PARI

sumNsq(n)= { for(x=1,n,r=floor(sqrt(x));sq=r*(r+1)*(2*r+1)/6;sn=x*(x+1)/2; print1(sn-sq",")) }

Python

from math import isqrt
def A000330(n): return n*(n+1)*(2*n+1)//6
def A132295(n): return n*(n+1)//2-A000330(isqrt(n)) # Jason Yuen, Jan 30 2024

Formula

Let r = floor(sqrt(n)). Then a(n) = n(n+1)/2 - r(r+1)(2r+1)/6.

Extensions

Definition corrected by R. J. Mathar, Sep 10 2016