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Consider the array T(n, m) where the n-th row is the sequence of integer coefficients of A(x), where 1<=a(n)<=n, such that A(x)^(1/n) consists entirely of integer coefficients and where m is the (m+1)-th coefficient. This is the table in the example of A112283 read term by term, row by row.
1

%I #7 Jan 27 2014 17:20:42

%S 1,1,1,2,1,1,3,3,1,1,4,2,4,3,4,4,4,1,1,5,5,5,5,1,1,6,3,2,3,6,6,6,3,4,

%T 6,6,6,6,3,4,6,6,3,6,6,2,3,6,6,6,3,4,6,6,2,6,6,6,6,6,6,6,3,4,6,6,4,6,

%U 6,2,6,6,4,6,3,2,3,6,6,6,3,4,3,6,3,6,3,4,6,6,2,6,3,6,3,6,1,1,7,7,7,7,7,7,1

%N Consider the array T(n, m) where the n-th row is the sequence of integer coefficients of A(x), where 1<=a(n)<=n, such that A(x)^(1/n) consists entirely of integer coefficients and where m is the (m+1)-th coefficient. This is the table in the example of A112283 read term by term, row by row.

%H Robert G. Wilson v, <a href="/A141524/b141524.txt">Table of n, for n = 1..55976</a>.

%e 1, 1,

%e 1, 2, 1,

%e 1, 3, 3, 1,

%e 1, 4, 2, 4, 3, 4, 4, 4, 1,

%e 1, 5, 5, 5, 5, 1,

%e 1, 6, 3, 2, 3, 6, 6, 6, 3, 4, 6, 6, 6, 6, 3, 4, 6, 6, 3, 6, 6, 2, 3, 6, 6, 6, 3, 4, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 3, 4, 6, 6, 4, 6, 6, 2, 6, 6, 4, 6, 3, 2, 3, 6, 6, 6, 3, 4, 3, 6, 3, 6, 3, 4, 6, 6, 2, 6, 3, 6, 3, 6, 1,

%e 1, 7, 7, 7, 7, 7, 7, 1,

%e etc.

%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++ ]; Table[a[i], {i, 0, j}]]; Table[ f[n], {n, 65}] // Flatten

%Y Cf. A111603, A111604, A112283.

%K nonn,tabf,look

%O 1,4

%A _Paul D. Hanna_ & _Robert G. Wilson v_, Aug 08 2008