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 A353504 #6 May 20 2022 08:51:33
%S A353504 0,0,1,1,1,2,2,4,4,6,6,8,9,11,12,14,14,18,21,23,26,29,29,33,36,39,40,
%T A353504 43,44,50,53,55,59,65,69,72,78,79,81,85,92,95,97,100,103,108,109,112,
%U A353504 118,124,129,137,139,142,149,155,159,165,166,173,178,181,187
%N A353504 Number of integer partitions of n whose product is less than the product of their multiplicities.
%e A353504 The a(2) = 1 through a(9) = 6 partitions:
%e A353504 11 111 1111 2111 21111 22111 221111 222111
%e A353504 11111 111111 31111 311111 411111
%e A353504 211111 2111111 2211111
%e A353504 1111111 11111111 3111111
%e A353504 21111111
%e A353504 111111111
%t A353504 Table[Length[Select[IntegerPartitions[n],Times@@#<Times@@Length/@Split[#]&]],{n,0,30}]
%Y A353504 LHS (product of parts) is counted by A339095, ranked by A003963.
%Y A353504 RHS (product of multiplicities) is counted by A266477, ranked by A005361.
%Y A353504 The version for greater instead of less is A353505.
%Y A353504 The version for equal instead of less is A353506, ranked by A353503.
%Y A353504 A181819 gives prime shadow, with an inverse A181821.
%Y A353504 A353398 counts partitions with the same product of multiplicities as of shadows, ranked by A353399.
%Y A353504 Cf. A002033, A008284, A085629, A097318, A098859, A114640, A116608, A118914, A124010, A304678, A353394, A353500, A353507.
%K A353504 nonn
%O A353504 0,6
%A A353504 _Gus Wiseman_, May 19 2022