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 A111603 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 antidiagonal read from upper right to lower left. 4
 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 3, 4, 1, 1, 2, 1, 2, 5, 1, 1, 2, 3, 4, 5, 6, 1, 1, 1, 3, 3, 5, 3, 7, 1, 1, 2, 3, 4, 5, 2, 7, 8, 1, 1, 2, 3, 4, 1, 3, 7, 4, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 3, 1, 5, 6, 7, 2, 3, 5, 11, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 1, 1, 3, 4, 5, 3, 1, 4, 9, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS EXAMPLE Table begins k= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 n\ 1| 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2| 1 2 1 2 2 2 1 2 2 2 1 2 1 2 3| 1 3 3 1 3 3 3 3 3 3 3 3 1 3 4| 1 4 2 4 3 4 4 4 1 4 4 4 3 4 5| 1 5 5 5 5 1 5 5 5 5 4 5 5 5 6| 1 6 3 2 3 6 6 6 3 4 6 6 6 6 7| 1 7 7 7 7 7 7 1 7 7 7 7 7 7 8| 1 8 4 8 2 8 4 8 7 8 8 8 4 8 9| 1 9 9 3 9 9 3 9 9 1 9 9 6 9 10| 1 10 5 10 10 2 5 10 10 10 3 10 5 10 11| 1 11 11 11 11 11 11 11 11 11 11 1 11 11 12| 1 12 6 4 9 12 4 12 12 8 6 12 6 12 13| 1 13 13 13 13 13 13 13 13 13 13 13 13 1 14| 1 14 7 14 7 14 14 2 7 14 14 14 14 14 15| 1 15 15 5 15 3 10 15 15 10 15 15 5 15 16| 1 16 8 16 4 16 8 16 10 16 8 16 12 16 MATHEMATICA f[n_] := f[n] = Block[{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]; Table[ a[j], {j, 0, 32}]]; g[n_, m_] := f[n][[m]]; Flatten[ Table[ f[i, n - i], {n, 15}, {i, n - 1, 1, -1}]] CROSSREFS Cf. A111613, A083952, A083953, A083954, A083945, A083946, A083947, A083948, A083949, A083950, A084066, A084067. Cf. A109626, A111604. Sequence in context: A101950 A104562 A164306 * A180178 A136178 A047140 Adjacent sequences:  A111600 A111601 A111602 * A111604 A111605 A111606 KEYWORD nonn,tabl AUTHOR Paul D. Hanna and Robert G. Wilson v, Aug 01 2005 STATUS approved

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Last modified February 23 12:03 EST 2019. Contains 320431 sequences. (Running on oeis4.)