

A141524


Consider the array T(n, m) where the nth 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



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, 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, 1, 7, 7, 7, 7, 7, 7, 1
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OFFSET

1,4


LINKS

Robert G. Wilson v, Table of n, for n = 1..55976.


EXAMPLE

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, 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,
1, 7, 7, 7, 7, 7, 7, 1,
etc.


MATHEMATICA

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


CROSSREFS

Cf. A111603, A111604, A112283.
Sequence in context: A125605 A110570 A082905 * A192650 A178059 A116188
Adjacent sequences: A141521 A141522 A141523 * A141525 A141526 A141527


KEYWORD

nonn,tabf,look


AUTHOR

Paul D. Hanna & Robert G. Wilson v, Aug 08 2008


STATUS

approved



