A071090 Sum of middle divisors of n.

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, 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, 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

Offset: 1

Author

N. J. A. Sloane, May 27 2002

Keywords

• nonn
• easy

Comments

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

Row sums of A299761. - Omar E. Pol, Jun 11 2022

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A067742, A071561, A071562, A299761, A302433.

Programs

Maple

A071090 := proc(n)
    a := 0 ;
    for d in numtheory[divisors](n) do
        if d^2 >= n/2 and d^2 < n*2 then
            a := a+d ;
        end if;
    end do:
    a;
end proc: # R. J. Mathar, Jun 18 2015

Mathematica

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

PARI

a(n)=sumdiv(n,d, if(d^2>=n/2 && d^2<2*n, d, 0)) \\ Charles R Greathouse IV, Aug 01 2016

Formula

a(n) = A000203(n) - A302433(n). - Omar E. Pol, Jun 11 2022