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A113308
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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 integers are counted separately.
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1
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1, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 8, 1, 7, 4, 10, 1, 13, 1, 15, 6, 11, 1, 27, 2, 13, 8, 28, 1, 27, 1, 36, 10, 17, 4, 62, 1, 19, 12, 59, 1, 47, 1, 66, 19, 23, 1, 118, 2, 31, 16, 91, 1, 78, 8, 117, 18, 29, 1, 193, 1, 31, 26, 159, 10, 115, 1, 153, 22, 51, 1, 320, 1, 37, 35, 190, 6, 161, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Sequence's terms calculated by "Max".
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FORMULA
| a(n)=1 if n=1 or is a prime, a(2)=2 if n is the square of a prime. (Robert G. Wilson v)
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EXAMPLE
| 6 = 1*1*1*1*1*1*(1+1+1+1+1+1) = 1*2*(1+2) = 2*1*(2+1). So a(6) = 3.
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MATHEMATICA
| (* first do *) Needs["DiscreteMath`Combinatorica`"] ( then *) t = Table[1, {80}]; Do[k = 1; lmt = PartitionsP@n; p = Partitions@n; While[k < lmt, a = Plus @@ p[[k]]*Times @@ p[[k]]; If[a < 81, t[[a]] += Length@ Permutations@ p[[k]]]; k++ ], {n, 40}]; t (from Robert G. Wilson v (rgwv(at)rgwv.com), May 03 2006)
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CROSSREFS
| Cf. A113309.
Sequence in context: A055440 A101279 A064576 * A143862 A115118 A115121
Adjacent sequences: A113305 A113306 A113307 * A113309 A113310 A113311
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Oct 25 2005
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