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%I #6 Nov 01 2021 19:22:13
%S 1,1,1,3,1,6,1,39,4,8,1,330,1,10,9,12495,1,1446,1,1620,11,14,1,
%T 1792050,6,16,580,10158,1,53002,1,2516534175,15,20,13,469241466,1,22,
%U 17,774558756,1,1696170,1,712914,20160,26,1,108457624531554,8,328588,21,6383964
%N a(1) = 1; a(n) = Sum_{d|n, d < n} d * a(d)^(n/d).
%F For n > 1, a(n) is the coefficient of x^n/n in expansion of -log(Product_{k=1..n-1} (1 - a(k)*x^k)).
%t a[1] = 1; a[n_] := a[n] = Sum[If[d < n, d a[d]^(n/d), 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 52}]
%Y Cf. A006241, A008578 (positions of 1's), A157313, A165552, A196545, A281145.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, Oct 28 2021
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