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A141524 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.

%I A141524 #7 Jan 27 2014 17:20:42
%S A141524 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 A141524 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 A141524 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 A141524 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 A141524 Robert G. Wilson v, <a href="/A141524/b141524.txt">Table of n, for n = 1..55976</a>.
%e A141524 1, 1,
%e A141524 1, 2, 1,
%e A141524 1, 3, 3, 1,
%e A141524 1, 4, 2, 4, 3, 4, 4, 4, 1,
%e A141524 1, 5, 5, 5, 5, 1,
%e A141524 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 A141524 1, 7, 7, 7, 7, 7, 7, 1,
%e A141524 etc.
%t A141524 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 A141524 Cf. A111603, A111604, A112283.
%K A141524 nonn,tabf,look
%O A141524 1,4
%A A141524 _Paul D. Hanna_ & _Robert G. Wilson v_, Aug 08 2008