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A117134
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Greatest k such that n^k divides (n^2)!.
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0
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3, 4, 7, 6, 17, 8, 21, 20, 24, 12, 70, 14, 32, 55, 63, 18, 80, 20, 99, 73, 48, 24, 191, 78, 56, 121, 130, 30, 224, 32, 204, 108, 72, 203, 323, 38, 80, 126, 398, 42, 293, 44, 193, 505, 96, 48, 575, 200, 312, 162, 225, 54, 485, 302, 522, 180, 120, 60, 898, 62, 128, 660, 682
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| If p is prime, a(p) = p+1, a(p^2) = floor((p^3 + p^2 + p + 1)/2)
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REFERENCES
| Thread "100!" in rec.puzzles newsgroup, April 2007
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EXAMPLE
| a(3)=4 because (3^2)! = 362880 = 3^4 * 4480 and 4480 is not divisible by 3
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MAPLE
| seq(ordp((n^2)!, n), n=2..50);
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CROSSREFS
| Cf. A011776.
Sequence in context: A077580 A069213 A130700 * A095001 A068905 A021746
Adjacent sequences: A117131 A117132 A117133 * A117135 A117136 A117137
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KEYWORD
| nonn
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AUTHOR
| Robert B. Israel (israel(AT)math.ubc.ca), Apr 26 2007
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