A116901 Number of partitions of n into at least two parts such that the product of largest and smallest part does not exceed n.

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

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 * A350846 A244487 A290962

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