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A034891
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Number of different products of partitions of n; number of partitions of n into prime parts (1 included); number of distinct orders of Abelian subgroups of symmetric group S_n.
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9
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1, 1, 2, 3, 4, 6, 8, 11, 14, 18, 23, 29, 36, 45, 55, 67, 81, 98, 117, 140, 166, 196, 231, 271, 317, 369, 429, 496, 573, 660, 758, 869, 993, 1133, 1290, 1465, 1662, 1881, 2125, 2397, 2699, 3035, 3407, 3820, 4276, 4780, 5337, 5951, 6628, 7372, 8191, 9090
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| G.f.: (1/(1-x))*(1/Product_{k>0} (1-x^prime(k))). a(n) = (1/n)*Sum_{k=1..n} A074372(k)*a(n-k). Partial sums of A000607. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 19 2002
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MATHEMATICA
| Table[ Length[ Union[ Apply[ Times, Partitions[ n ], 1 ] ] ], {n, 30} ]
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CROSSREFS
| Cf. A000792, A000793, A009490.
Sequence in context: A114829 A175869 A007279 * A143611 A062464 A053270
Adjacent sequences: A034888 A034889 A034890 * A034892 A034893 A034894
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be)
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs)
a(0)=1 from Michael Somos Feb 05 2011
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