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A067538 Number of partitions of n in which the number of parts divides n. +0
2
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)
OFFSET

1,2

COMMENT

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]

LINKS

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]

FORMULA

a(p) = 2 for all primes p.

EXAMPLE

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}.

MATHEMATICA

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)

CROSSREFS

Cf. A000041.

Sequence in context: A100577 A018818 A157019 this_sequence A096154 A084540 A113416

Adjacent sequences: A067535 A067536 A067537 this_sequence A067539 A067540 A067541

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto (n_nomoto(AT)yabumi.com), Jan 27 2002

EXTENSIONS

Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 16 2002

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Last modified December 7 08:40 EST 2009. Contains 170430 sequences.


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