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Search: id:A102067
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| A102067 |
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Numbers n such that n does not divide P(n)! even though P(n)^2 is not a factor of n, where P(n) is the largest prime factor of n. |
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3
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| 12, 24, 45, 48, 80, 90, 96, 135, 160, 175, 180, 189, 192, 224, 240, 270, 320, 350, 360, 378, 384, 405, 448, 480, 525, 539, 540, 567, 637, 640, 672, 700, 720, 756, 768, 810, 875, 896, 945, 960
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Clearly, if P(n)^2 is a factor of n, then n does not divide P(n)!. Each member shows that the converse is false.
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REFERENCES
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I. Kastanas, The smallest factorial that is a multiple of n, Amer. Math. Monthly 101 (1994) 179.
A. J. Kempner, Miscellanea, Amer. Math. Monthly, 25 (1918), 201-210. See Section II, "Concerning the smallest integer m! divisible by a given integer n."
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LINKS
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Eric Weisstein's World of Mathematics, GreatestPrimeFactor
Index entries for sequences related to factorial numbers.
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EXAMPLE
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12 does not divide P(12)! = 3!, and 3^2 is not a factor of 12.
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CROSSREFS
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n is a member if and only if n is in A057109 but not in A070003. See also A006530, A102068.
Adjacent sequences: A102064 A102065 A102066 this_sequence A102068 A102069 A102070
Sequence in context: A053990 A026365 A051435 this_sequence A081808 A080495 A090776
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KEYWORD
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nonn
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 28 2004
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