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Search: id:A086435
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| A086435 |
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Maximum number of parts possible in a factorization of n into a product of distinct numbers > 1. |
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+0
4
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| 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 3, 1, 2, 2, 3, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 2, 3, 1, 3, 2, 2, 1, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 3
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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For n>1, a((n+1)!) = n is the first occurrence of n in the sequence. This function depends only on the prime signature of n. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 19 2006
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LINKS
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Eric Weisstein's World of Mathematics, UnorderedFactorization
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EXAMPLE
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a(6)=2 since 6 may be factored into distinct parts as {{2,3},{6}}, so the largest number of factors possible is 2.
a(8)=2 since 8 may be factored into distinct parts as {{8},{2,4}}, so the largest numbers of factors possible is 2.
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PROGRAM
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(PARI) { a(n, m=1) = if(n>m, 1 + vecmax( apply( x->if(x>m, a(n/x, x)), divisors(n) ))) } [From Max Alekseyev (maxale(AT)gmail.com), Jul 16 2009]
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CROSSREFS
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Cf. A000142, A025487.
Sequence in context: A065031 A058061 A064547 this_sequence A099305 A033109 A111627
Adjacent sequences: A086432 A086433 A086434 this_sequence A086436 A086437 A086438
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Jul 19, 2003
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