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G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} sigma(k) * A(x)^k.
1

%I #12 Apr 22 2020 07:59:39

%S 1,-3,14,-82,546,-3932,29816,-234438,1893469,-15612527,130870098,

%T -1111844944,9552257052,-82846987926,724385135208,-6378457007916,

%U 56511184375548,-503399149941744,4505973904735072,-40508206566645846,365585085331313000,-3311041732282565260

%N G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} sigma(k) * A(x)^k.

%C Reversion of the sum of divisors function (A000203).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%t nmax = 22; CoefficientList[InverseSeries[Series[Sum[x^k/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x], x] // Rest

%Y Cf. A000203, A050389, A333957.

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, Apr 22 2020