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%I A112284 #11 Mar 15 2015 20:23:16
%S A112284 1,1,1,2,1,12,1,3,1,13,1,22,1,12,14,19,1,9,1,27,18,31,1,19,1,49,1,12,
%T A112284 1,59,1,17,61,27,15,14,1,98,6,7,1,12,1,95,45,9,1,17,1,26,73,23,1,18,
%U A112284 10,35,69,17,1,108,1,29,65,28,47
%N A112284 A112283/n.
%F A112284 Conjecture: a(n)=1 iff n is 1, a prime or the square of an odd prime.
%t A112284 f[n_] := Module[{j = 1, a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; While[a[j] != 1, j++ ]; j]; Table[ f[n]/n, {n, 10}]
%Y A112284 Cf. A109626, A112283.
%K A112284 hard,nonn
%O A112284 1,4
%A A112284 _Paul D. Hanna_ and _Robert G. Wilson v_, Aug 20 2005
%E A112284 a(30)-a(50) from _Robert G. Wilson v_, Oct 29 2007
%E A112284 a(51)-a(65) from _Robert G. Wilson v_, Jul 25 2008

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