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A237984 Number of partitions of n whose mean is a part. 20
1, 2, 2, 3, 2, 5, 2, 6, 5, 8, 2, 21, 2, 14, 22, 30, 2, 61, 2, 86, 67, 45, 2, 283, 66, 80, 197, 340, 2, 766, 2, 663, 543, 234, 703, 2532, 2, 388, 1395, 4029, 2, 4688, 2, 4476, 7032, 1005, 2, 17883, 2434, 9713, 7684, 14472, 2, 25348, 17562, 37829, 16786, 3721 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = 2 if and only if n is a prime.

LINKS

Table of n, a(n) for n=1..58.

FORMULA

a(n) = A000041(n) - A327472(n). - Gus Wiseman, Sep 14 2019

EXAMPLE

a(6) counts these partitions:  6, 33, 321, 222, 111111.

From Gus Wiseman, Sep 14 2019: (Start)

The a(1) = 1 through a(10) = 8 partitions (A = 10):

  1  2   3    4     5      6       7        8         9          A

     11  111  22    11111  33      1111111  44        333        55

              1111         222              2222      432        22222

                           321              3221      531        32221

                           111111           4211      111111111  33211

                                            11111111             42211

                                                                 52111

                                                                 1111111111

(End)

MATHEMATICA

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Mean[p]]], {n, 40}]

CROSSREFS

Cf. A238478.

The Heinz numbers of these partitions are A327473.

A similar sequence for subsets is A065795.

Dominated by A067538.

The strict case is A240850.

Partitions without their mean are A327472.

Cf. A000016, A316413, A324753, A325705, A327478, A327482.

Sequence in context: A164896 A298422 A304716 * A118136 A258567 A076396

Adjacent sequences:  A237981 A237982 A237983 * A237985 A237986 A237987

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 27 2014

STATUS

approved

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Last modified November 12 19:24 EST 2019. Contains 329077 sequences. (Running on oeis4.)