cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A336866 #5 Aug 10 2020 22:15:43
%S A336866 0,0,0,1,1,2,4,5,9,15,21,28,46,56,80,114,149,192,269,337,455,584,751,
%T A336866 943,1234,1527,1944,2422,3042,3739,4699,5722,7100,8668,10634,12880,
%U A336866 15790,19012,23093,27776,33528,40102,48264,57469,68793,81727,97372,115227
%N A336866 Number of integer partitions of n without all distinct multiplicities.
%F A336866 a(n) = A000041(n) - A098859(n).
%e A336866 The a(0) = 0 through a(9) = 15 partitions (empty columns shown as dots):
%e A336866   .  .  .  (21)  (31)  (32)  (42)    (43)    (53)     (54)
%e A336866                        (41)  (51)    (52)    (62)     (63)
%e A336866                              (321)   (61)    (71)     (72)
%e A336866                              (2211)  (421)   (431)    (81)
%e A336866                                      (3211)  (521)    (432)
%e A336866                                              (3221)   (531)
%e A336866                                              (3311)   (621)
%e A336866                                              (4211)   (3321)
%e A336866                                              (32111)  (4221)
%e A336866                                                       (4311)
%e A336866                                                       (5211)
%e A336866                                                       (32211)
%e A336866                                                       (42111)
%e A336866                                                       (222111)
%e A336866                                                       (321111)
%t A336866 Table[Length[Select[IntegerPartitions[n],!UnsameQ@@Length/@Split[#]&]],{n,0,30}]
%Y A336866 A098859 counts the complement.
%Y A336866 A130092 gives the Heinz numbers of these partitions.
%Y A336866 A001222 counts prime factors with multiplicity.
%Y A336866 A013929 lists nonsquarefree numbers.
%Y A336866 A047966 counts uniform partitions.
%Y A336866 A047967 counts non-strict partitions.
%Y A336866 A071625 counts distinct prime multiplicities.
%Y A336866 A130091 lists numbers with distinct prime multiplicities.
%Y A336866 A181796 counts divisors with distinct prime multiplicities.
%Y A336866 A327498 gives the maximum divisor with distinct prime multiplicities.
%Y A336866 Cf. A000009, A000041, A008284, A116608, A118914, A124010, A242882, A255231, A325280, A325242, A329739, A336422, A336571.
%K A336866 nonn
%O A336866 0,6
%A A336866 _Gus Wiseman_, Aug 09 2020