cp's OEIS Frontend

A317258 Heinz numbers of integer partitions that are not totally nonincreasing.

%I A317258 #5 Jul 27 2018 00:26:40
%S A317258 18,50,54,75,90,98,108,126,147,150,162,180,198,234,242,245,250,252,
%T A317258 270,294,300,306,324,338,342,350,363,375,378,396,414,450,468,486,490,
%U A317258 500,507,522,525,540,550,558,578,588,594,600,605,612,630,648,650,666,684
%N A317258 Heinz numbers of integer partitions that are not totally nonincreasing.
%C A317258 An integer partition is totally nonincreasing if either it is empty or a singleton or its multiplicities (where if x < y the multiplicity of x is counted prior to the multiplicity of y) are weakly decreasing and are themselves a totally nonincreasing integer partition.
%C A317258 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A317258 Sequence of all integer partitions that are not totally nonincreasing begins: (221), (331), (2221), (332), (3221), (441), (22211), (4221), (442), (3321), (22221), (32211), (5221), (6221), (551), (443), (3331), (42211), (32221), (4421), (33211), (7221), (222211), (661), (8221), (4331), (552), (3332), (42221), (52211), (9221), (33221).
%t A317258 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A317258 totincQ[q_]:=Or[Length[q]<=1,And[OrderedQ[Length/@Split[q]],totincQ[Reverse[Length/@Split[q]]]]];
%t A317258 Select[Range[1000],!totincQ[Reverse[primeMS[#]]]&]
%Y A317258 Cf. A056239, A071365, A100883, A112769, A181819, A182850, A242031, A296150, A305733, A317256, A317257.
%K A317258 nonn
%O A317258 1,1
%A A317258 _Gus Wiseman_, Jul 25 2018