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A117753
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Triangular array based on multiplication of A034386 and A117682 and the factorial function modulo the factorial function.
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0
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0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 6, 6, 12, 6, 12, 0, 0, 0, 0, 0, 0, 24, 24, 48, 24, 144, 0, 576, 210, 210, 420, 210, 1260, 0, 0, 3780, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1728, 1728, 3456, 1728, 10368, 207360, 41472, 0, 0, 82944, 210, 210, 420, 210, 1260, 25200, 5040, 44100, 1209600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| This triangular array is organized like a group multiplication table.
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FORMULA
| f[n_, 1] = cf[n]; f[n_, 2] = p[n]; f[n_, 3] = n!; a(n,m) = Mod[f[n, 1 + Mod[n, 3]]*f[m, 1 + Mod[m, 3]], n! ]
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EXAMPLE
| 0
0, 0
0, 0, 0
1, 1, 2, 1
6, 6, 12, 6, 12
0, 0, 0, 0, 0, 0
24, 24, 48, 24, 144, 0, 576
0, 0, 0, 0, 0, 0, 0, 0, 0
1728, 1728, 3456, 1728, 10368, 207360, 41472, 0, 0, 82944
210, 210, 420, 210, 1260, 25200, 5040, 44100, 1209600, 362880, 44100
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MATHEMATICA
| Clear[f, g, cf, p, a, b] f[n_] := If[PrimeQ[n] == True, 1, n] cf[0] = 1; cf[n_Integer?Positive] := cf[n] = f[n]*cf[n - 1] g[n_] := If[PrimeQ[n] == True, n, 1] p[0] = 1; p[n_Integer?Positive] := p[n] = g[n]*p[n - 1] f[n_, 1] = cf[n]; f[n_, 2] = p[n]; f[n_, 3] = n!; a = Table[Table[Mod[f[n, 1 + Mod[n, 3]]*f[m, 1 + Mod[m, 3]], n! ], {m, 0, n}], {n, 0, 10}] Flatten[a]
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CROSSREFS
| Cf. A034386 and A117682.
Sequence in context: A193561 A117965 A111646 * A145883 A062820 A113336
Adjacent sequences: A117750 A117751 A117752 * A117754 A117755 A117756
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Apr 14 2006
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