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A325457 Heinz numbers of integer partitions with strictly decreasing differences.

%I A325457 #4 May 03 2019 21:25:59
%S A325457 1,2,3,4,5,6,7,9,10,11,13,14,15,17,18,19,21,22,23,25,26,29,31,33,34,
%T A325457 35,37,38,39,41,43,46,47,49,50,51,53,55,57,58,59,61,62,65,67,69,70,71,
%U A325457 73,74,75,77,79,82,83,85,86,87,89,91,93,94,95,97,98
%N A325457 Heinz numbers of integer partitions with strictly decreasing differences.
%C A325457 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325457 The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (-3,-2).
%C A325457 The enumeration of these partitions by sum is given by A320470.
%H A325457 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325457 The sequence of terms together with their prime indices begins:
%e A325457    1: {}
%e A325457    2: {1}
%e A325457    3: {2}
%e A325457    4: {1,1}
%e A325457    5: {3}
%e A325457    6: {1,2}
%e A325457    7: {4}
%e A325457    9: {2,2}
%e A325457   10: {1,3}
%e A325457   11: {5}
%e A325457   12: {1,1,2}
%e A325457   13: {6}
%e A325457   14: {1,4}
%e A325457   15: {2,3}
%e A325457   17: {7}
%e A325457   19: {8}
%e A325457   20: {1,1,3}
%e A325457   21: {2,4}
%e A325457   22: {1,5}
%e A325457   23: {9}
%t A325457 primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A325457 Select[Range[100],Greater@@Differences[primeptn[#]]&]
%Y A325457 Cf. A056239, A112798, A320470, A320510, A325328, A325352, A325360, A325361, A325368, A325399, A325456, A325461, A320470, A325396.
%K A325457 nonn
%O A325457 1,2
%A A325457 _Gus Wiseman_, May 03 2019