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A018783
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Number of partitions of n into parts having a common factor.
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7
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0, 0, 1, 1, 2, 1, 4, 1, 5, 3, 8, 1, 14, 1, 16, 9, 22, 1, 38, 1, 45, 17, 57, 1, 94, 7, 102, 30, 138, 1, 218, 1, 231, 58, 298, 21, 451, 1, 491, 103, 644, 1, 919, 1, 1005, 203, 1256, 1, 1784, 15, 1993, 299, 2439, 1, 3365, 62, 3735, 492, 4566, 1, 6252, 1, 6843, 819, 8349, 107, 11096
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..10000
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FORMULA
| a(n) = -Sum_{d|n, d<n} moebius(n/d)*A000041(d) = A000041(n) - A000837(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 17 2003
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MAPLE
| with (numtheory): with (combinat):
a:= n-> `if`(n=0, 0,
numbpart(n) -add (mobius(n/d) *numbpart(d), d=divisors(n))):
seq (a(n), n=0..100); # Alois P. Heinz, Nov 29 2011
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CROSSREFS
| Cf. A083710.
Sequence in context: A093890 A006306 A083711 * A200976 A114326 A060680
Adjacent sequences: A018780 A018781 A018782 * A018784 A018785 A018786
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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