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A106847
a(n) = Sum {k + j*m <= n} (k + j*m), with 0 < k,j,m <= n.
4
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
FORMULA
From Ridouane Oudra, Jun 02 2024: (Start)
a(n) = (1/2)*Sum_{k=1..n} (n^2 + n - k^2 - k)*tau(k);
a(n) = (1/2)*(n^2 + n)*A006218(n) - Sum_{k=1..n} A143272(k);
a(n) = (1/2)*((n + 1)*A143274(n) - A143127(n) - A319085(n)). (End)
a(n) ~ n^3 * (log(n) + 2*gamma - 4/3)/3, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jun 15 2024
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
KEYWORD
nonn
AUTHOR
Ralf Stephan, May 06 2005
STATUS
approved