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 A300383 #15 Apr 04 2025 11:39:46
%S A300383 1,1,2,1,3,2,5,1,3,3,7,2,11,5,5,1,15,3,22,3,8,7,30,2,6,11,4,5,42,5,56,
%T A300383 1,11,15,11,3,77,22,17,3,101,8,135,7,7,30,176,2,14,6,23,11,231,4,15,5,
%U A300383 33,42,297,5,385,56,11,1,23,11,490,15,45,11,627,3
%N A300383 In the ranked poset of integer partitions ordered by refinement, a(n) is the size of the lower ideal generated by the partition with Heinz number n.
%C A300383 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). The size of the corresponding upper ideal is A317141(n). Chains are A213427(n) and maximal chains are A002846(n).
%H A300383 Robert Price, <a href="/A300383/b300383.txt">Table of n, a(n) for n = 1..350</a>
%F A300383 a(prime(n)) = A000041(n).
%F A300383 a(x * y) <= a(x) * a(y).
%e A300383 The a(30) = 5 partitions are (321), (2211), (3111), (21111), (111111), with corresponding Heinz numbers: 30, 36, 40, 48, 64.
%t A300383 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A300383 Table[Length[Union[Sort/@Join@@@Tuples[IntegerPartitions/@primeMS[n]]]],{n,50}]
%Y A300383 Cf. A000041, A001055, A001222, A002846, A056239, A112798, A213427, A215366, A265947, A296150, A299200, A299202, A299925, A300273.
%Y A300383 Cf. A317141, A317142, A317143.
%K A300383 nonn
%O A300383 1,3
%A A300383 _Gus Wiseman_, Mar 04 2018