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Search: id:A113309
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| A113309 |
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a(n) = the number of finite sequences of positive integers {b(k)} where (product b(k))* (sum b(k)) = n. Different orderings of the same sequence {b(k)} are not counted separately. |
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+0
2
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| 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 4, 2, 2, 1, 5, 2, 2, 2, 4, 1, 5, 1, 4, 2, 2, 2, 7, 1, 2, 2, 5, 1, 5, 1, 4, 3, 2, 1, 9, 2, 3, 2, 4, 1, 6, 2, 7, 2, 2, 1, 8, 1, 2, 4, 7, 2, 5, 1, 4, 2, 5, 1, 11, 1, 2, 3, 4, 2, 5, 1, 9, 4, 2, 1, 10, 2, 2, 2, 7, 1, 9, 2, 4, 2, 2, 2, 13, 1, 3, 4, 7, 1, 5, 1, 7
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Sequence's terms calculated by "Max".
First occurrence: 1, 4, 12, 16, 24, 54, 36, 60, 48, 84, 72, 108, 96, ..., . - Robert G. Wilson v (rgwv(at)rgwv.com), May 03 2006
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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a(n)=1 iff n=1 or n is a prime. a(n)=2 if n is a semiprime. - Robert G. Wilson v (rgwv(at)rgwv.com), May 03 2006
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EXAMPLE
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6 = 1*1*1*1*1*1*(1+1+1+1+1+1) = 1*2*(1+2). So a(6) = 2.
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MATHEMATICA
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(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) t = Table[1, {104}]; Do[k = 1; lmt = PartitionsP[n]; p = Partitions[n]; While[k < lmt, a = Plus @@ p[[k]]*Times @@ p[[k]]; If[a < 105, t[[a]]++ ]; k++ ], {n, 52}]; t - Robert G. Wilson v (rgwv(at)rgwv.com), May 03 2006
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CROSSREFS
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Cf. A113308.
Sequence in context: A122375 A038548 A068108 this_sequence A062362 A084113 A115751
Adjacent sequences: A113306 A113307 A113308 this_sequence A113310 A113311 A113312
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet, Oct 25 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), May 03 2006
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