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a(n) = Sum_{d|n} d * binomial(d+n/d-1, d).
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%I #15 Apr 22 2021 09:08:03

%S 1,4,6,14,10,36,14,56,48,80,22,228,26,140,240,316,34,552,38,820,546,

%T 308,46,2088,680,416,1044,2156,58,4380,62,3248,1782,680,4690,9672,74,

%U 836,2808,14560,82,15456,86,9108,17040,1196,94,37704,12110,21420,5916,16068,106,44496

%N a(n) = Sum_{d|n} d * binomial(d+n/d-1, d).

%F G.f.: Sum_{k >= 1} k * x^k/(1 - x^k)^(k+1).

%F If p is prime, a(p) = 2*p.

%t a[n_] := DivisorSum[n, # * Binomial[# + n/# - 1, #] &]; Array[a, 100] (* _Amiram Eldar_, Apr 22 2021 *)

%o (PARI) a(n) = sumdiv(n, d, d*binomial(d+n/d-1, d));

%o (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-x^k)^(k+1)))

%Y Cf. A081543, A343574.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Apr 22 2021