A356131 a(n) = Sum_{k=1..n} (k - 1)^n * binomial(floor(n/k)+1,2).
0, 1, 9, 100, 1302, 20648, 377022, 7921039, 186926431, 4916562309, 142373072781, 4506381442625, 154721361953489, 5729251983077521, 227585590018322461, 9654855432715969784, 435659531345223039702, 20836069677785611552293
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := Sum[(k - 1)^n * Binomial[Floor[n/k]+1, 2], {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Jul 28 2022 *) -
PARI
a(n) = sum(k=1, n, (k-1)^n*binomial((n\k)+1, 2));
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PARI
a(n) = sum(k=1, n, k*(sigma(k, n-1)-(n\k)^n));
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PARI
a(n) = sum(k=1, n, k*sumdiv(k, d, (d-1)^n/d));