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Search: id:A034258
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| A034258 |
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Write n! as a product of n numbers, n = k(1)*k(2)*...*k(n) with k(1)<=k(2)<=..., in all possible ways; a(n) = max value of k(1). |
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3
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| 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 15, 15, 15, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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36, 49, 52 and 55 are not in this sequence. - Don Reble (djr(AT)nk.ca), Nov 29 2001
a(n) >= a(n-1). - Larry Reeves (larryr(AT)acm.org), Jan 06 2005
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REFERENCES
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R. K. Guy and J. L. Selfridge, Factoring factorial n, Amer. Math. Monthly, 105 (1998), 766-767.
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EXAMPLE
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3! = 6 = 1*2*3 is the only possible factorization, so a(3) = 1.
27! = 8^4 * 9^6 * 10^6 * 11^2 * 12 * 13^2 * 14^3 * 17 * 19 * 23, with 4 + 6 + 6 + 2 + 1 + 2 + 3 + 1 + 1 + 1 = 27 factors, which is the required number. Since the first factor is 8, a(27) >= 8. In fact no larger value can be obtained and a(27) = 8.
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CROSSREFS
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Cf. A034259, A034260.
Sequence in context: A060384 A105564 A025811 this_sequence A090663 A111890 A104277
Adjacent sequences: A034255 A034256 A034257 this_sequence A034259 A034260 A034261
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 12 2001
Verified by Don Reble (djr(AT)nk.ca), Apr 22 2007
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