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A070039
Sum of the divisors of n that are < sqrt(n).
49
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
1,6
LINKS
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, d<sqrt(n)} d. - Wesley Ivan Hurt, Jun 17 2023
EXAMPLE
a(96) = 1+2+3+4+6+8+12 = 36; a(225) = 1+3+5+9 = 18.
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, #&, #<Sqrt[n]&], {n, 100}] (* Harvey P. Dale, Oct 26 2015 *)
PROG
(PARI) a(n)=if(n<1, 0, sumdiv(n, d, (d^2<n)*d)) /* Michael Somos, Nov 19 2005 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 19 2002
STATUS
approved