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A325460 Heinz numbers of integer partitions with strictly increasing differences (with the last part taken to be 0).

%I A325460 #4 May 31 2019 03:44:36
%S A325460 1,2,3,5,7,10,11,13,14,17,19,22,23,26,29,31,33,34,37,38,39,41,43,46,
%T A325460 47,51,53,57,58,59,61,62,67,69,71,73,74,79,82,83,85,86,87,89,93,94,95,
%U A325460 97,101,103,106,107,109,111,113,115,118,122,123,127,129,130,131
%N A325460 Heinz numbers of integer partitions with strictly increasing differences (with the last part taken to be 0).
%C A325460 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325460 The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) (with the last part taken to be 0) are (-3,-2,-1).
%C A325460 The enumeration of these partitions by sum is given by A179269.
%H A325460 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325460 The sequence of terms together with their prime indices begins:
%e A325460     1: {}
%e A325460     2: {1}
%e A325460     3: {2}
%e A325460     5: {3}
%e A325460     7: {4}
%e A325460    10: {1,3}
%e A325460    11: {5}
%e A325460    13: {6}
%e A325460    14: {1,4}
%e A325460    17: {7}
%e A325460    19: {8}
%e A325460    22: {1,5}
%e A325460    23: {9}
%e A325460    26: {1,6}
%e A325460    29: {10}
%e A325460    31: {11}
%e A325460    33: {2,5}
%e A325460    34: {1,7}
%e A325460    37: {12}
%e A325460    38: {1,8}
%t A325460 primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A325460 Select[Range[100],Less@@Differences[Append[primeptn[#],0]]&]
%Y A325460 A subsequence of A005117.
%Y A325460 Cf. A007294, A056239, A112798, A179269, A325327, A325362, A325364, A325367, A325388, A325390, A325395, A325398, A325456, A325461.
%K A325460 nonn
%O A325460 1,2
%A A325460 _Gus Wiseman_, May 03 2019