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

Author

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

Keywords

• nonn

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, ...,.

Crossrefs

Cf. A111603, A112283.

Programs

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}]

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.

Extensions

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