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%I A326121 #9 Sep 10 2019 19:55:58
%S A326121 0,1,1,5,1,18,1,33,28,58,1,246,1,178,369,577,1,1539,1,2774,2531,2170,
%T A326121 1,16706,3126,8362,20413,35366,1,116444,1,135425,178479,131362,94933,
%U A326121 1110999,1,524650,1596521,2530946,1,7280892,1,8403734,16364457,8389138,1,78568322,823544,43420683
%N A326121 Expansion of Sum_{k>=1} k^2 * x^(2*k) / (1 - k * x^k).
%F A326121 a(n) = Sum_{d|n, d>1} (n/d)^d = Sum_{d|n, d<n} d^(n/d).
%F A326121 a(p) = 1, where p is prime.
%F A326121 a(n) = A055225(n) - n.
%t A326121 nmax = 50; CoefficientList[Series[Sum[k^2 x^(2 k)/(1 - k x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A326121 Table[DivisorSum[n, (n/#)^# &, # > 1 &], {n, 1, 50}]
%o A326121 (PARI) a(n)={sumdiv(n, d, if(d > 1, (n/d)^d))} \\ _Andrew Howroyd_, Sep 10 2019
%Y A326121 Cf. A055225, A078308, A087909.
%K A326121 nonn
%O A326121 1,4
%A A326121 _Ilya Gutkovskiy_, Sep 10 2019

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