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A112285
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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.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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, ...,.
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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.
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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}]
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CROSSREFS
| Cf. A111603, A112283.
Sequence in context: A191700 A000643 A196265 * A037170 A006399 A056800
Adjacent sequences: A112282 A112283 A112284 * A112286 A112287 A112288
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)AT)juno.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 29 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 25 2008
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