A326850 - OEIS

%I #9 Dec 17 2020 05:41:51

%S 0,1,1,1,1,1,2,1,2,1,3,1,4,1,5,2,6,1,10,1,10,5,12,1,23,1,18,15,23,1,

%T 49,1,34,36,38,1,106,1,54,79,81,1,189,1,124,162,104,1,412,1,145,307,

%U 289,1,608,12,437,559,256,1,1432,1,340,981,976,79,1730,1

%N Number of strict integer partitions of n whose maximum part divides n.

%H Fausto A. C. Cariboni, <a href="/A326850/b326850.txt">Table of n, a(n) for n = 0..300</a>

%e The initial terms count the following partitions:

%e    1: (1)

%e    2: (2)

%e    3: (3)

%e    4: (4)

%e    5: (5)

%e    6: (6)

%e    6: (3,2,1)

%e    7: (7)

%e    8: (8)

%e    8: (4,3,1)

%e    9: (9)

%e   10: (10)

%e   10: (5,4,1)

%e   10: (5,3,2)

%e   11: (11)

%e   12: (12)

%e   12: (6,5,1)

%e   12: (6,4,2)

%e   12: (6,3,2,1)

%e   13: (13)

%e   14: (14)

%e   14: (7,6,1)

%e   14: (7,5,2)

%e   14: (7,4,3)

%e   14: (7,4,2,1)

%e   15: (15)

%e   15: (5,4,3,2,1)

%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Divisible[n,Max[#]]&]],{n,0,30}]

%Y Positions of 1's appear to be A308168.

%Y The non-strict case is given by A067538.

%Y Cf. A018818, A033630, A067538, A102627, A200745, A316413, A326625, A326836, A326843, A326851.

%K nonn

%O 0,7

%A _Gus Wiseman_, Jul 28 2019