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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

%I

%S 0,0,1,2,4,5,8,12,18,25,35,47,66,87,118,155,207,264,348,443,571,725,

%T 923,1155,1466,1821,2275,2821,3501,4293,5307,6477,7933,9658,11750,

%U 14198,17251,20746,24986,30009,36024,42983,51446,61176,72839,86497,102538

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

%C 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

%H Alois P. Heinz, <a href="/A116901/b116901.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%Y Cf. A000041, A116900, A116902, A240200.

%K nonn

%O 0,4

%A _Giovanni Resta_, Mar 14 2006

%E More terms from _Robert G. Wilson v_, Mar 15 2006

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)