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Search: id:A144300
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| A144300 |
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a(n) = P(n)-d(n) = number of partitions of n, minus number of divisors of n. |
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+0
4
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| 0, 0, 1, 2, 5, 7, 13, 18, 27, 38, 54, 71, 99, 131, 172, 226, 295, 379, 488, 621, 788, 998, 1253, 1567, 1955, 2432, 3006, 3712, 4563, 5596, 6840, 8343, 10139, 12306, 14879, 17968, 21635, 26011, 31181, 37330, 44581, 53166, 63259, 75169, 89128
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n) is also the number of partitions of n whose parts are not equal.
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LINKS
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O. E. Pol, The shell model of partitions
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FORMULA
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a(n) = A000041(n)-A000005(n).
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MAPLE
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with (numtheory): b:= proc(n) option remember; `if`(n=0, 1, add (add (d, d=divisors(j)) *b(n-j), j=1..n)/n) end: a:= n-> b(n)- tau(n): seq (a(n), n=1..50); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 07 2008]
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CROSSREFS
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Cf. A000005, A000041, A135010, A138121.
Sequence in context: A092059 A023229 A160676 this_sequence A045353 A038985 A109652
Adjacent sequences: A144297 A144298 A144299 this_sequence A144301 A144302 A144303
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KEYWORD
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easy,nonn
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AUTHOR
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Omar E. Pol (info(AT)polprimos.com), Sep 17 2008
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