OFFSET
0,6
COMMENTS
These are partitions where no part appears fewer times than all of the others.
EXAMPLE
The partition (4,2,2,1) has least multiplicity 1, and two parts of multiplicity 1 (namely 1 and 4), so is counted under a(9).
The a(3) = 1 through a(9) = 14 partitions:
(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)
(42111)
(222111)
(321111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Count[Length/@Split[#], Min@@Length/@Split[#]]>1&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 30 2023
STATUS
approved