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Search: id:A101048
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| A101048 |
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Number of partitions of n into semiprimes (a)0) = 1 by convention). |
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+0
7
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| 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 3, 2, 3, 1, 5, 3, 5, 4, 7, 4, 9, 7, 10, 8, 13, 10, 17, 13, 18, 17, 25, 21, 29, 25, 34, 34, 43, 37, 51, 49, 61, 59, 73, 69, 89, 87, 103, 103, 124, 122, 148, 149, 172, 176, 206, 208, 244, 248, 281, 293, 337, 344, 391, 405, 456, 479, 537, 553
(list; graph; listen)
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OFFSET
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0,11
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COMMENT
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Semiprime analogue of A000607. a(n) <= A002095(n). - Jonathan Vos Post (jvospost2(AT)yahoo.com), Oct 01 2007
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
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G.f. = 1/product(product(1-x^(p(i)p(j)), i = 1..j),j = 1..infinity), p(k) is the k-th prime. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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EXAMPLE
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a(12) = #{6 + 6, 4 + 4 + 4} = #{2 * (2*3), 3 * (2*2)} = 2.
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MAPLE
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g:=1/product(product(1-x^(ithprime(i)*ithprime(j)), i=1..j), j=1..30): gser:=series(g, x=0, 75): seq(coeff(gser, x, n), n=1..71); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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CROSSREFS
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Cf. A000041, A000607, A101049, A001358, A064911, A002095.
Cf. A112020, A112021.
Adjacent sequences: A101045 A101046 A101047 this_sequence A101049 A101050 A101051
Sequence in context: A080233 A097808 A114325 this_sequence A070102 A029182 A035373
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 28 2004
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EXTENSIONS
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a(0) set to 1 by njas, Nov 23 2007
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