cp's OEIS Frontend

A071090 Sum of middle divisors of n.

%I A071090 #21 Jun 13 2022 03:05:10
%S A071090 1,1,0,2,0,5,0,2,3,0,0,7,0,0,8,4,0,3,0,9,0,0,0,10,5,0,0,11,0,11,0,4,0,
%T A071090 0,12,6,0,0,0,13,0,13,0,0,14,0,0,14,7,5,0,0,0,15,0,15,0,0,0,16,0,0,16,
%U A071090 8,0,17,0,0,0,17,0,23,0,0,0,0,18,0,0,18,9,0,0,19,0,0,0,19,0,19,20,0,0
%N A071090 Sum of middle divisors of n.
%C A071090 Divisors are in the half-open interval [sqrt(n/2), sqrt(n*2)).
%C A071090 Row sums of A299761. - _Omar E. Pol_, Jun 11 2022
%H A071090 R. J. Mathar, <a href="/A071090/b071090.txt">Table of n, a(n) for n = 1..1000</a>
%F A071090 a(n) = A000203(n) - A302433(n). - _Omar E. Pol_, Jun 11 2022
%p A071090 A071090 := proc(n)
%p A071090     a := 0 ;
%p A071090     for d in numtheory[divisors](n) do
%p A071090         if d^2 >= n/2 and d^2 < n*2 then
%p A071090             a := a+d ;
%p A071090         end if;
%p A071090     end do:
%p A071090     a;
%p A071090 end proc: # _R. J. Mathar_, Jun 18 2015
%t A071090 Table[Plus @@ Select[ Divisors[n], Sqrt[n/2] <= # < Sqrt[n*2] &], {n, 1, 95}]
%o A071090 (PARI) a(n)=sumdiv(n,d, if(d^2>=n/2 && d^2<2*n, d, 0)) \\ _Charles R Greathouse IV_, Aug 01 2016
%Y A071090 Cf. A000203, A067742, A071561, A071562, A299761, A302433.
%K A071090 nonn,easy
%O A071090 1,4
%A A071090 _N. J. A. Sloane_, May 27 2002