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Search: id:A107329
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| A107329 |
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Triangle read by rows: T(n,k) gives number of partitions of k,(k=1..n) into the prime factors of n. |
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+0
1
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| 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0
(list; table; graph; listen)
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OFFSET
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2,20
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COMMENT
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T(n,n) equals A066882. Table begins at n=2 since 1 has no valid prime decomposition: {0, 1}, {0, 0, 1}, {0, 1, 0, 1}, {0, 0, 0, 0, 1}, {0, 1, 1, 1, 1, 2}, {0, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 1, 0, 1}, {0, 0, 1, 0, 0, 1, 0, 0, 1}
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FORMULA
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T(n, k) is factor of x^k in 1/Product( 1-x^p_i) with p_i the prime factors of n.
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EXAMPLE
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T(30,12)=5 counting [2,2,2,2,2,2], [2,2,2,3,3], [3,3,3,3], [2,2,3,5] and [2,5,5].
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MATHEMATICA
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Table[Rest@CoefficientList[Series[1/Times @@ ((1-x^#)& /@ (First /@ FactorInteger[n])), {x, 0, n}], x], {n, 2, 24}]
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CROSSREFS
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Cf. A066882.
Adjacent sequences: A107326 A107327 A107328 this_sequence A107330 A107331 A107332
Sequence in context: A096562 A096563 A078359 this_sequence A085859 A086016 A103270
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 22 2005
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