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A116901 Number of partitions of n into at least two parts such that the product of largest and smallest part does not exceed n. 6
0, 0, 1, 2, 4, 5, 8, 12, 18, 25, 35, 47, 66, 87, 118, 155, 207, 264, 348, 443, 571, 725, 923, 1155, 1466, 1821, 2275, 2821, 3501, 4293, 5307, 6477, 7933, 9658, 11750, 14198, 17251, 20746, 24986, 30009, 36024, 42983, 51446, 61176, 72839, 86497, 102538 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of partitions p of n such that mean(p) >= multiplicity(max(p)).  For example, a(5) counts these 5 partitions:  5, 41, 32, 311, 2111. See the Mathematica program at A240200 for a count of partitions defined in this manner, along with related sequences. - Clark Kimberling, Apr 03 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

a(4) = 4 since property holds for 4 partitions of 4: (3,1), (2,2), (2,1,1), (1,1,1,1).

MATHEMATICA

f[n_] := Length@ Select[ IntegerPartitions@n, (Length@ # > 1 && Last@# First@# <= n) &]; Array[f, 46] (* Robert G. Wilson v, Mar 15 2006 *)

CROSSREFS

Cf. A000041, A116900, A116902, A240200.

Sequence in context: A039842 A188216 A238395 * A244487 A290962 A334522

Adjacent sequences:  A116898 A116899 A116900 * A116902 A116903 A116904

KEYWORD

nonn

AUTHOR

Giovanni Resta, Mar 14 2006

EXTENSIONS

More terms from Robert G. Wilson v, Mar 15 2006

STATUS

approved

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Last modified November 29 06:00 EST 2021. Contains 349416 sequences. (Running on oeis4.)