A112285 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 row sum of A to the first coefficient of one.

2, 4, 8, 27, 22, 340, 44, 156, 62, 1065, 112, 2467, 158, 1914, 2551, 4234, 274, 2161, 344, 8643, 6611, 12696, 508, 8410, 522, 28171, 566, 7500, 814, 39433, 932, 15000, 57160, 26980, 15681, 13590, 1334, 121327, 7786, 8908, 1642, 15896, 1808, 150069, 74267, 16105, 2164

Offset

1,1

Comments

mod(a(n),n):0,0,2,3,2,4,2,4,8,5,2,7,2,10,1,10,2,1,2,3,17,2,2,10,22,13,26,24,2, ...,.

The sum of just the even terms of T(n,k): 0,2,0,22,0,290,0,144,0,900,0,2288,0,1606,332,4124,0,1708,0,7908,790,10940,0,8196,0,24168,0,6920,0, ...,.

Links

Table of n, a(n) for n=1..47.

Formula

Sum_{m=0..k} from T(n, m), k is the least k>0 such that T(n, m)=1.

Sum_{m=0..A112283(n)} T(n, m).

a(p)=p(p-1)+2.

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++ ]; Sum[ a[i], {i, 0, j}]]; Do[ Print[ f[n]], {n, 29}]

Crossrefs

Cf. A111603, A112283.

Sequence in context: A286936 A323948 A196265 * A037170 A212409 A006399

Adjacent sequences: A112282 A112283 A112284 * A112286 A112287 A112288

Keyword

nonn

Author

Paul D. Hanna and Robert G. Wilson v, Aug 29 2005

Extensions

More terms from Robert G. Wilson v, Jul 25 2008

Status

approved