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

1,4

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

Formula

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

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}]

Prog

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

Crossrefs

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

Sequence in context: A066442 A171388 A086134 * A105221 A215339 A061376

Adjacent sequences: A071087 A071088 A071089 * A071091 A071092 A071093

Keyword

nonn,easy

Author

N. J. A. Sloane, May 27 2002

Status

approved