A112283 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 sequence is the first occurrence of 1 after the first column.

1, 2, 3, 8, 5, 72, 7, 24, 9, 130, 11, 264, 13, 168, 210, 304, 17, 162, 19, 540, 378, 682, 23, 456, 25, 1274, 27, 336, 29, 1770, 31, 544, 2013, 918, 525, 504, 37, 3724, 234, 280, 41, 504, 43, 4180, 2025, 414, 47, 816, 49, 1300, 3723, 1196, 53, 972, 550, 1960, 3933, 986, 59, 6480, 61, 1798, 4095, 1792, 3055

Offset

1,2

Comments

The degree >0 of the polynomial above whose coefficient is 1.

Links

Table of n, a(n) for n=1..65.

Formula

Conjecture: a(n)=n if n is 1, a prime or the square of the odd primes.

Example

Only the pertinent part of the 'Table' in A109626.
{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, ..., },
{1, 7, 7, 7, 7, 7, 7, 1},
{1, 8, 4, 8, 2, 8, 4, 8, 7, 8, 8, 8, 4, 8, 8, 8, 3, 8, 8, 8, 2, 8, 8, 8, 1},
{1, 9, 9, 3, 9, 9, 3, 9, 9, 1},
{1, 10, 5, 10, 10, 2, 5, 10, 10, 10, 3, 10, 5, 10, ..., },
{1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1},
{1, 12, 6, 4, 9, 12, 4, 12, 12, 8, 6, 12, 6, 12, ..., },
{1, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 1}, ...,.

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++ ]; j]; Table[ f[n], {n, 10}]

Crossrefs

Cf. A109626, A112284.

Sequence in context: A369740 A109844 A128779 * A136182 A170911 A067911

Adjacent sequences: A112280 A112281 A112282 * A112284 A112285 A112286

Keyword

nonn

Author

Paul D. Hanna and Robert G. Wilson v, Aug 20 2005

Extensions

a(30)-a(50) from Robert G. Wilson v, Oct 29 2007

a(51)-a(65) from Robert G. Wilson v, Jul 25 2008

Status

approved