cp's OEIS Frontend

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

%I A070039 #30 Jun 27 2025 01:01:46
%S A070039 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 A070039 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 A070039 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 A070039 Sum of the divisors of n that are < sqrt(n).
%H A070039 G. C. Greubel, <a href="/A070039/b070039.txt">Table of n, a(n) for n = 1..5000</a>
%F A070039 a(n) = sigma(n) - A070038(n).
%F A070039 a(n) = Sum_{n>=1} n*x^(n^2+n)/(1-x^n). - _Vladeta Jovovic_, Feb 09 2005
%F A070039 a(n) = Sum_{d|n, d<sqrt(n)} d. - _Wesley Ivan Hurt_, Jun 17 2023
%F A070039 a(n) = A066839(n) - A037213(n). - _Ridouane Oudra_, Jun 24 2025
%e A070039 a(96) = 1+2+3+4+6+8+12 = 36; a(225) = 1+3+5+9 = 18.
%p A070039 seq(add(d, d in select(x->x^2<n, numtheory[divisors](n))), n=1..100); # _Ridouane Oudra_, Jun 24 2025
%t A070039 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 A070039 Table[DivisorSum[n,#&,#<Sqrt[n]&],{n,100}] (* _Harvey P. Dale_, Oct 26 2015 *)
%o A070039 (PARI) a(n)=if(n<1, 0, sumdiv(n,d, (d^2<n)*d)) /* _Michael Somos_, Nov 19 2005 */
%Y A070039 Cf. A038548, A000203, A000005, A070038, A056924.
%K A070039 nonn
%O A070039 1,6
%A A070039 _Labos Elemer_, Apr 19 2002