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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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10
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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
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OFFSET
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0,3
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COMMENTS
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a(n) = length of n-th row in A212721. - Reinhard Zumkeller, Jun 14 2012
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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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, Sep 19 2002
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MAPLE
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b:= proc(n, i) option remember; local p;
p:= `if`(i<1, 1, ithprime(i));
`if`(n=0, 1, `if`(i<0, 0, b(n, i-1)+
`if`(p>n, 0, b(n-p, i))))
end:
a:= n-> b(n, numtheory[pi](n)):
seq(a(n), n=1..100); # Alois P. Heinz, Feb 15 2013
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MATHEMATICA
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Table[ Length[ Union[ Apply[ Times, Partitions[ n ], 1 ] ] ], {n, 30} ]
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PROG
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(Haskell)
a034891 = length . a212721_row -- Reinhard Zumkeller, Jun 14 2012
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CROSSREFS
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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
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nonn,easy,nice,changed
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AUTHOR
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Wouter Meeussen
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs)
a(0)=1 from Michael Somos Feb 05 2011
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STATUS
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approved
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