A070039 Sum of the divisors of n that are < sqrt(n).

0, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 6, 1, 3, 4, 3, 1, 6, 1, 7, 4, 3, 1, 10, 1, 3, 4, 7, 1, 11, 1, 7, 4, 3, 6, 10, 1, 3, 4, 12, 1, 12, 1, 7, 9, 3, 1, 16, 1, 8, 4, 7, 1, 12, 6, 14, 4, 3, 1, 21, 1, 3, 11, 7, 6, 12, 1, 7, 4, 15, 1, 24, 1, 3, 9, 7, 8, 12, 1, 20, 4, 3, 1, 23, 6, 3, 4, 15, 1, 26, 8, 7, 4, 3, 6

Offset: 1

Author

Labos Elemer, Apr 19 2002

Keywords

• nonn

Examples

			a(96) = 1+2+3+4+6+8+12 = 36; a(225) = 1+3+5+9 = 18.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A038548, A000203, A000005, A070038, A056924.

Programs

Maple

seq(add(d, d in select(x->x^2Ridouane Oudra, Jun 24 2025

Mathematica

di[x_] := Divisors[x] lds[x_] := Ceiling[DivisorSigma[0, x]/2] rd[x_] := Reverse[Divisors[x]] td[x_] := Table[Part[rd[x], w], {w, 1, lds[x]}] sud[x_] := Apply[Plus, td[x]] Table[DivisorSigma[1, w]-sud[w], {w, 1, 128}]
Table[DivisorSum[n,#&,#Harvey P. Dale, Oct 26 2015 *)

PARI

a(n)=if(n<1, 0, sumdiv(n,d, (d^2Michael Somos, Nov 19 2005 */

Formula

a(n) = sigma(n) - A070038(n).

a(n) = Sum_{n>=1} n*x^(n^2+n)/(1-x^n). - Vladeta Jovovic, Feb 09 2005

a(n) = Sum_{d|n, dWesley Ivan Hurt, Jun 17 2023

a(n) = A066839(n) - A037213(n). - Ridouane Oudra, Jun 24 2025