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Search: id:A067538
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| A067538 |
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Number of partitions of n in which the number of parts divides n. |
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+0
2
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| 1, 2, 2, 4, 2, 8, 2, 11, 9, 14, 2, 46, 2, 24, 51, 66, 2, 126, 2, 202, 144, 69, 2, 632, 194, 116, 381, 756, 2, 1707, 2, 1417, 956, 316, 2043, 5295, 2, 511, 2293, 9151, 2, 10278, 2, 8409, 14671, 1280, 2, 36901, 8035, 21524, 11614, 25639, 2, 53138, 39810, 85004
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also sum of p(n,d) over the divisors d of n, where p(n,m) is the count of partitions of n in exactly m parts. [From Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 07 2009]
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LINKS
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Wouter Meeussen, Table of n, a(n) for n = 1..500
Weisstein, Eric W. "Partition Function P." [From Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 07 2009]
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FORMULA
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a(p) = 2 for all primes p.
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EXAMPLE
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a(3)=2 because 3 is a prime; a(4)=4 because the five partitions of 4 are {4}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1} and all are divisible by the number of terms except {2, 1, 1}.
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MATHEMATICA
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Needs["DiscreteMath`Combinatorica`"]; Do[p = Partitions[n]; l = Length[p]; c = 0; k = 1; While[k < l + 1, If[ IntegerQ[ n/Length[ p[[k]] ]], c++ ]; k++ ]; Print[c], {n, 1, 57}]
Contribution from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 07 2009: (Start)
p[n_, k_]:=p[n, k]=p[n-1, k-1]+p[n-k, k]; p[n_, k_]:=0/; k>n; p[n_, n_]:=1; p[n_, 0]:=0
Table[Plus @@ (p[n, # ]&/ @ Divisors[n]), {n, 36}] (End)
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CROSSREFS
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Cf. A000041.
Sequence in context: A100577 A018818 A157019 this_sequence A096154 A084540 A113416
Adjacent sequences: A067535 A067536 A067537 this_sequence A067539 A067540 A067541
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KEYWORD
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easy,nonn
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AUTHOR
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Naohiro Nomoto (n_nomoto(AT)yabumi.com), Jan 27 2002
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EXTENSIONS
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Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 16 2002
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