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a(n) = Sum_{d divides n} d*(n/d)^(d-1).
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%I #9 Sep 03 2019 12:08:14

%S 1,3,4,9,6,25,8,49,37,101,12,373,14,477,496,1313,18,3907,20,6941,5272,

%T 11309,24,49321,3151,53301,59320,144789,30,468181,32,657473,649936,

%U 1114181,121416,5124961,38,4980813,6909280,13756761,42,44768725,44

%N a(n) = Sum_{d divides n} d*(n/d)^(d-1).

%H Seiichi Manyama, <a href="/A167531/b167531.txt">Table of n, a(n) for n = 1..5000</a>

%F G.f.: Sum{k>0} x^k/(1-k*x^k)^2.

%o (PARI) a(n)=sumdiv(n,d,d*(n/d)^(d-1))

%o (PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, x^k/(1-k*x^k)^2)) \\ _Seiichi Manyama_, Sep 03 2019

%Y Cf. A055225, A324158.

%K nonn

%O 1,2

%A _Franklin T. Adams-Watters_, Nov 05 2009