%I #4 May 02 2019 16:04:36

%S 1,2,3,4,5,6,7,8,9,11,13,15,16,17,18,19,21,23,25,27,29,30,31,32,35,37,

%T 41,43,47,49,53,54,55,59,61,64,65,67,71,73,75,77,79,81,83,89,91,97,

%U 101,103,105,107,109,113,119,121,125,127,128,131,133,137,139

%N Heinz numbers of integer partitions whose differences (with the last part taken to be zero) are weakly decreasing.

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%C The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (x, y, z) are (y - x, z - y). We adhere to this standard for integer partitions also even though they are always weakly decreasing. For example, the differences of (6,3,1) (with the last part taken to be 0) are (-3,-2,-1).

%C The enumeration of these partitions by sum is given by A320509.

%H Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>

%t primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];

%t Select[Range[100],GreaterEqual@@Differences[Append[primeptn[#],0]]&]

%Y Cf. A056239, A112798, A320348, A320466, A320509, A325327, A325361, A325364, A325367, A325389, A325390, A325397.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 02 2019