|
%I #8 Feb 20 2021 16:09:37
%S 1,1,2,2,3,2,5,2,5,3,5,2,21,2,5,6,9,2,22,2,21,6,5,2,134,3,5,6,23,2,
%T 157,2,27,6,5,6,478,2,5,6,208,2,224,2,31,63,5,2,1720,3,30,6,34,2,322,
%U 6,295,6,5,2,13899,2,5,68,126,8,429,2,42,6,358,2,19959,2
%N Number of integer partitions of n whose parts all divide n and whose length also divides n.
%C The Heinz numbers of these partitions are given by A326847.
%H Fausto A. C. Cariboni, <a href="/A326842/b326842.txt">Table of n, a(n) for n = 0..419</a>
%e The a(1) = 1 through a(8) = 5 partitions:
%e (1) (2) (3) (4) (5) (6) (7) (8)
%e (11) (111) (22) (11111) (33) (1111111) (44)
%e (1111) (222) (2222)
%e (321) (4211)
%e (111111) (11111111)
%e The a(12) = 21 partitions:
%e (12)
%e (6,6)
%e (4,4,4)
%e (6,3,3)
%e (6,4,2)
%e (3,3,3,3)
%e (4,3,3,2)
%e (4,4,2,2)
%e (4,4,3,1)
%e (6,2,2,2)
%e (6,3,2,1)
%e (6,4,1,1)
%e (2,2,2,2,2,2)
%e (3,2,2,2,2,1)
%e (3,3,2,2,1,1)
%e (3,3,3,1,1,1)
%e (4,2,2,2,1,1)
%e (4,3,2,1,1,1)
%e (4,4,1,1,1,1)
%e (6,2,1,1,1,1)
%e (1,1,1,1,1,1,1,1,1,1,1,1)
%t Table[Length[Select[IntegerPartitions[n,All,Divisors[n]],Divisible[n,Length[#]]&]],{n,1,30}]
%Y Partitions using divisors are A018818.
%Y Partitions whose length divides their sum are A067538.
%Y Cf. A047993, A102627, A316413, A326841, A326843, A326847.
%K nonn
%O 0,3
%A _Gus Wiseman_, Jul 26 2019
|
