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 A109626 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 lower left to upper right. 25
 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 3, 2, 1, 1, 5, 2, 1, 2, 1, 1, 6, 5, 4, 3, 2, 1, 1, 7, 3, 5, 3, 3, 1, 1, 1, 8, 7, 2, 5, 4, 3, 2, 1, 1, 9, 4, 7, 3, 1, 4, 3, 2, 1, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 11, 5, 3, 2, 7, 6, 5, 1, 3, 1, 1, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 13, 6, 11, 10, 9, 4, 1, 3, 5 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Table of n, a(n) for n=1..101. 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[ g[i, n - i], {n, 15}, {i, n - 1, 1, -1}]] CROSSREFS Rows: A111613, A083952, A083953, A083954, A083945, A083946, A083947, A083948, A083949, A083950, A084066, A084067. Columns: A111613, A111627, A026741, A051176, A111607, A060791, A111608, A106608, A111609, A111610, A111611, A106612, A106614, A106618, A106620. Diagonals: main=A000027, first upper=A111614, 2nd=A111627, 3rd=A111615, first lower=A111618, 2nd=A111623. Other diagonals: T(2n-1, n)=A005408, A111626, A111627, A111628, A111629, A111630. Cf. A111603, A111604. Sequence in context: A239454 A108888 A124021 * A182285 A160182 A195825 Adjacent sequences: A109623 A109624 A109625 * A109627 A109628 A109629 KEYWORD nonn,tabl AUTHOR Paul D. Hanna and Robert G. Wilson v, Aug 01 2005 STATUS approved

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Last modified July 24 13:53 EDT 2024. Contains 374584 sequences. (Running on oeis4.)