A336866 Number of integer partitions of n without all distinct multiplicities.

0, 0, 0, 1, 1, 2, 4, 5, 9, 15, 21, 28, 46, 56, 80, 114, 149, 192, 269, 337, 455, 584, 751, 943, 1234, 1527, 1944, 2422, 3042, 3739, 4699, 5722, 7100, 8668, 10634, 12880, 15790, 19012, 23093, 27776, 33528, 40102, 48264, 57469, 68793, 81727, 97372, 115227

Offset: 0

Author

Gus Wiseman, Aug 09 2020

Keywords

• nonn

Examples

			The a(0) = 0 through a(9) = 15 partitions (empty columns shown as dots):
  .  .  .  (21)  (31)  (32)  (42)    (43)    (53)     (54)
                       (41)  (51)    (52)    (62)     (63)
                             (321)   (61)    (71)     (72)
                             (2211)  (421)   (431)    (81)
                                     (3211)  (521)    (432)
                                             (3221)   (531)
                                             (3311)   (621)
                                             (4211)   (3321)
                                             (32111)  (4221)
                                                      (4311)
                                                      (5211)
                                                      (32211)
                                                      (42111)
                                                      (222111)
                                                      (321111)
		

Crossrefs

A098859 counts the complement.

A130092 gives the Heinz numbers of these partitions.

A001222 counts prime factors with multiplicity.

A013929 lists nonsquarefree numbers.

A047966 counts uniform partitions.

A047967 counts non-strict partitions.

A071625 counts distinct prime multiplicities.

A130091 lists numbers with distinct prime multiplicities.

A181796 counts divisors with distinct prime multiplicities.

A327498 gives the maximum divisor with distinct prime multiplicities.

Cf. A000009, A000041, A008284, A116608, A118914, A124010, A242882, A255231, A325280, A325242, A329739, A336422, A336571.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],!UnsameQ@@Length/@Split[#]&]],{n,0,30}]

Formula

a(n) = A000041(n) - A098859(n).