A356127 a(n) = Sum_{k=1..n} k^k * binomial(floor(n/k)+1,2).
1, 7, 37, 305, 3435, 50163, 873713, 17651465, 405072044, 10405078324, 295716748946, 9211817291426, 312086923883692, 11424093751088836, 449317984131957736, 18896062057875064856, 846136323944211829050, 40192544399241524385636
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := Sum[k^k * 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^k*binomial(n\k+1, 2));
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PARI
a(n) = sum(k=1, n, k*sumdiv(k, d, d^(d-1)));
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-x^k)^2)/(1-x))
Formula
a(n) = Sum_{k=1..n} k * Sum_{d|k} d^(d-1).
G.f.: (1/(1-x)) * Sum_{k>=1} (k * x)^k/(1 - x^k)^2.