A116902 Number of partitions of n into at least two parts such that the product of largest and smallest part exceeds n.

0, 0, 0, 0, 1, 2, 2, 3, 4, 6, 8, 10, 13, 16, 20, 23, 32, 36, 46, 55, 66, 78, 99, 108, 136, 160, 188, 216, 271, 296, 364, 415, 484, 559, 684, 725, 890, 1028, 1175, 1313, 1599, 1727, 2084, 2335, 2636, 3019, 3620, 3801, 4553, 5170, 5819, 6460, 7690, 8265, 9728, 10783

Offset

1,6

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..200

Example

a(9)=4 since property holds for 4 partitions of 9: {7,2}, {6,3}, {5,4}, {5,2,2}.

Mathematica

fun[n_]:=Select[IntegerPartitions[n], (Length[ # ]>1 && Last[ # ]First[ # ]>n)&]; Table[Length[fun[k]], {k, 40}]
(* second program: *)
A[n_] := Length@ Select[ IntegerPartitions@n, Length@# > 1 && Last@# First@# > n &]; Array[A, 56] (* Robert G. Wilson v, Apr 06 2006 *)

Crossrefs

Cf. A000041, A116900, A116901.

Sequence in context: A114541 A077114 A118246 * A066447 A035542 A225484

Adjacent sequences: A116899 A116900 A116901 * A116903 A116904 A116905

Keyword

nonn

Author

Giovanni Resta, Mar 14 2006

Extensions

More terms from Robert G. Wilson v, Apr 06 2006

Status

approved