%I #11 Mar 15 2015 20:23:16

%S 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 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 10,35,69,17,1,108,1,29,65,28,47

%N A112283/n.

%F Conjecture: a(n)=1 iff n is 1, a prime or the square of an odd prime.

%t 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 Cf. A109626, A112283.

%K hard,nonn

%O 1,4

%A _Paul D. Hanna_ and _Robert G. Wilson v_, Aug 20 2005

%E a(30)-a(50) from _Robert G. Wilson v_, Oct 29 2007

%E a(51)-a(65) from _Robert G. Wilson v_, Jul 25 2008