A106847 a(n) = Sum {k + l*m <= n} (k + l*m), with 0 < k,l,m <= n.

0, 0, 2, 11, 31, 71, 131, 229, 357, 537, 767, 1064, 1412, 1867, 2385, 3000, 3720, 4570, 5506, 6608, 7808, 9194, 10734, 12436, 14260, 16360, 18622, 21079, 23739, 26668, 29758, 33199, 36815, 40742, 44924, 49369, 54085, 59265, 64661, 70355

Offset

0,3

Links

M. F. Hasler, Table of n, a(n) for n = 0..9999

Example

We have 1+1*1=2<=3, 1+2*1=3, 1+1*2=3, 2+1*1=3, thus a(3)=2+3+3+3=11.

Maple

A106847 := proc(n)
    local a, k, l, m ;
    a := 0 ;
    for k from 1 to n do
        for l from 1 to n-k do
            m := floor((n-k)/l) ;
            if m >=1 then
                m := min(m, n) ;
                a := a+m*k+l*m*(m+1)/2 ;
            end if;
        end do:
    end do:
    a ;
end proc: # R. J. Mathar, Oct 17 2012

Mathematica

A106847[n_] := Module[{a, k, l, m}, a = 0; For[k = 1, k <= n, k++, For[l = 1, l <= n - k, l++, If[l == 0, m = n, m = Floor[(n - k)/l]]; If[m >= 1, m = Min[m, n]; a = a + m*k + l*m*(m + 1)/2]]]; a];
Table[A106847[n], {n, 0, 40}] (* Jean-François Alcover, Apr 04 2024, after R. J. Mathar *)

Prog

(PARI) A106847(n)=sum(m=1, n-1, sum(k=1, (n-1)\m, (n-m*k)*(n+m*k+1)))/2  \\ M. F. Hasler, Oct 17 2012

Crossrefs

Cf. A106633, A106634, A106846, A078567 (number of terms).

Sequence in context: A085041 A197642 A121346 * A092761 A296733 A087933

Adjacent sequences: A106844 A106845 A106846 * A106848 A106849 A106850

Keyword

nonn

Author

Ralf Stephan, May 06 2005

Status

approved