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.
%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