A326852 - OEIS

%I #10 Feb 11 2021 01:49:18

%S 0,0,0,0,0,0,1,0,1,0,1,0,16,0,1,7,11,0,30,0,40,18,1,0,201,0,1,38,124,

%T 0,426,0,211,73,1,48,1391,0,1,131,1741,0,1774,0,951,2145,1,0,8345,0,

%U 1853,381,2382,0,6718,2761,10633,623,1,0,68037

%N Number of non-constant integer partitions of n whose length and maximum both divide n.

%C The Heinz numbers of these partitions are given by A326838.

%H Fausto A. C. Cariboni, <a href="/A326852/b326852.txt">Table of n, a(n) for n = 0..180</a>

%e The a(6) = 1 through a(16) = 11 partitions (empty columns not shown):

%e   (321)  (4211)  (52111)  (633)     (7211111)  (53322)  (8332)

%e                           (642)                (53331)  (8422)

%e                           (651)                (54222)  (8431)

%e                           (4332)               (54321)  (8521)

%e                           (4422)               (54411)  (8611)

%e                           (4431)               (55221)  (42222211)

%e                           (6222)               (55311)  (43222111)

%e                           (6321)                        (43321111)

%e                           (6411)                        (44221111)

%e                           (322221)                      (44311111)

%e                           (332211)                      (82111111)

%e                           (333111)

%e                           (422211)

%e                           (432111)

%e                           (441111)

%e                           (621111)

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

%Y The possibly constant case is A326843.

%Y The strict case is A326851.

%Y Cf. A018818, A047993, A067538, A326837, A326838, A326842, A326849.

%K nonn

%O 0,13

%A _Gus Wiseman_, Jul 26 2019