A071090 - OEIS

%I #21 Jun 13 2022 03:05:10

%S 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 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 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 Sum of middle divisors of n.

%C Divisors are in the half-open interval [sqrt(n/2), sqrt(n*2)).

%C Row sums of A299761. - _Omar E. Pol_, Jun 11 2022

%H R. J. Mathar, <a href="/A071090/b071090.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A000203(n) - A302433(n). - _Omar E. Pol_, Jun 11 2022

%p A071090 := proc(n)

%p     a := 0 ;

%p     for d in numtheory[divisors](n) do

%p         if d^2 >= n/2 and d^2 < n*2 then

%p             a := a+d ;

%p         end if;

%p     end do:

%p     a;

%p end proc: # _R. J. Mathar_, Jun 18 2015

%t Table[Plus @@ Select[ Divisors[n], Sqrt[n/2] <= # < Sqrt[n*2] &], {n, 1, 95}]

%o (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 Cf. A000203, A067742, A071561, A071562, A299761, A302433.

%K nonn,easy

%O 1,4

%A _N. J. A. Sloane_, May 27 2002