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A023895
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Number of partitions of n into composite parts.
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4
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1, 0, 0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 4, 1, 4, 2, 7, 2, 9, 3, 12, 6, 15, 6, 23, 11, 26, 15, 37, 19, 48, 26, 61, 39, 78, 47, 105, 65, 126, 88, 167, 111, 211, 146, 264, 196, 331, 241, 426, 318, 519, 408, 657, 511, 820, 651, 1010, 833, 1252, 1028, 1564, 1301, 1900
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| First differences of A002095. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 03 2006
a(n+1) > a(n) for n>108. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 22 2007
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 0..150
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FORMULA
| G.f.=(1-x)*product((1-x^p(j))/(1-x^j), j=1..infinity), where p(j) is the j-th prime. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 03 2006
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EXAMPLE
| a(12) = 4 because 12 = 4 + 4 + 4 = 6 + 6 = 4 + 8 = 12 (itself a composite number).
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MAPLE
| g:=(1-x)*product((1-x^ithprime(j))/(1-x^j), j=1..80): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..62); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 03 2006
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MATHEMATICA
| Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; CoefficientList[ Series[1/Product[1 - x^Composite[i], {i, 1, 50}], {x, 0, 75}], x]
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PROG
| (Haskell)
a023895 = p a002808_list where
p _ 0 = 1
p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Jan 15 2012
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CROSSREFS
| Cf. A002808.
Cf. A002095.
Cf. A132456.
Cf. A204389.
Sequence in context: A132456 A080966 A187150 * A070963 A174064 A139158
Adjacent sequences: A023892 A023893 A023894 * A023896 A023897 A023898
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 22 2007
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