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%I #27 Jun 17 2023 11:20:03
%S 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,
%T 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,
%U 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
%N Sum of the divisors of n that are < sqrt(n).
%H G. C. Greubel, <a href="/A070039/b070039.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) = sigma(n) - A070038(n).
%F a(n) = Sum_{n>=1} n*x^(n^2+n)/(1-x^n). - _Vladeta Jovovic_, Feb 09 2005
%F a(n) = Sum_{d|n, d<sqrt(n)} d. - _Wesley Ivan Hurt_, Jun 17 2023
%e a(96) = 1+2+3+4+6+8+12 = 36; a(225) = 1+3+5+9 = 18.
%t 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}]
%t Table[DivisorSum[n,#&,#<Sqrt[n]&],{n,100}] (* _Harvey P. Dale_, Oct 26 2015 *)
%o (PARI) a(n)=if(n<1, 0, sumdiv(n,d, (d^2<n)*d)) /* _Michael Somos_, Nov 19 2005 */
%Y Cf. A038548, A000203, A000005, A070038, A056924.
%K nonn
%O 1,6
%A _Labos Elemer_, Apr 19 2002
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