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A106847
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a(n) = Sum {k + j*m <= n} (k + j*m), with 0 < k,j,m <= n.
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4
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (1/2)*Sum_{k=1..n} (n^2 + n - k^2 - k)*tau(k);
a(n) ~ n^3 * (log(n) + 2*gamma - 4/3)/3, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jun 15 2024
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EXAMPLE
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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.
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MAPLE
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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 ;
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MATHEMATICA
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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];
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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