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Search: id:A101271
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| A101271 |
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Number of partitions of n into 3 distinct and relatively prime parts. |
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+0
2
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| 1, 1, 2, 3, 4, 5, 6, 8, 9, 12, 12, 16, 15, 21, 20, 26, 25, 33, 28, 40, 36, 45, 42, 56, 44, 65, 56, 70, 64, 84, 66, 96, 81, 100, 88, 120, 90, 133, 110, 132, 121, 161, 120, 175, 140, 176, 156, 208, 153, 220, 180, 222, 196, 261, 184, 280, 225, 270, 240, 312, 230, 341, 272
(list; graph; listen)
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OFFSET
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6,3
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FORMULA
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G.f. for the number of partitions of n into m distinct and relatively prime parts is Sum(moebius(k)*x^(m*(m+1)/2*k)/Product(1-x^(i*k), i=1..m), k=1..infinity).
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EXAMPLE
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For n=10 we have 4 such partitions: 1+2+7, 1+3+6, 1+4+5 and 2+3+5.
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MAPLE
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m:=3: with(numtheory): g:=sum(mobius(k)*x^(m*(m+1)/2*k)/Product(1-x^(i*k), i=1..m), k=1..20): gser:=series(g, x=0, 80): seq(coeff(gser, x^n), n=6..77); (Deutsch)
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CROSSREFS
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Cf. A023022-A023030, A000741-A000743, A023031-A023035.
Sequence in context: A011869 A134030 A100054 this_sequence A093110 A165707 A052063
Adjacent sequences: A101268 A101269 A101270 this_sequence A101272 A101273 A101274
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 19 2004
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 31 2005
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