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A122379
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Numbers n such that S(n)! > n^2 > P(n)!, where S(n)! is the smallest factorial divisible by n and P(n) is the greatest prime factor of n.
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4
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4, 9, 16, 18, 25, 27, 32, 50, 54, 64, 75, 81, 96, 98, 100, 108, 125, 128, 135, 147, 150, 160, 162, 175, 189, 192, 196, 200, 216, 225, 243, 245, 250, 256, 270, 294, 300, 324, 343, 350, 375, 378, 392, 400, 405, 432, 441, 450, 486, 490, 500, 512, 525, 540, 567
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| It is conjectured that n^2 < P(n)! for almost all n. It is known that S(n) = P(n) for almost all n. Clearly, S(n) >= P(n) for all n > 1.
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REFERENCES
| J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
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LINKS
| Index entries for sequences related to factorial numbers.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality
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EXAMPLE
| S(9)! = 6! = 720 > 81 = 9^2 > 6 = 3! = P(9)!, so 9 is a member.
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CROSSREFS
| Cf. A000290, A002034, A006530, A057109, A092495, A102068, A122378, A122380.
Sequence in context: A072903 A066926 A066925 * A104020 A066694 A102646
Adjacent sequences: A122376 A122377 A122378 * A122380 A122381 A122382
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KEYWORD
| nonn
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AUTHOR
| Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Sep 03 2006
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