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A144300
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Number of partitions of n minus number of divisors of n.
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6
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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; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(n) is also the number of partitions of n whose parts are not all equal.
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LINKS
| O. E. Pol, The shell model of partitions
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FORMULA
| a(n) = p(n) - d(n) = A000041(n)-A000005(n).
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MAPLE
| 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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PROG
| (PARI) al(n)=vector(n, k, numbpart(k)-numdiv(k))
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CROSSREFS
| Cf. A000005, A000041, A135010, A138121, A195364.
Sequence in context: A176983 A160676 A169690 * A045353 A038985 A109652
Adjacent sequences: A144297 A144298 A144299 * A144301 A144302 A144303
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KEYWORD
| easy,nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Sep 17 2008
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