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A325461 Heinz numbers of integer partitions with strictly decreasing differences (with the last part taken to be 0).

%I A325461 #7 May 03 2019 21:26:15
%S A325461 1,2,3,4,5,7,9,11,13,15,17,19,23,25,29,31,35,37,41,43,47,49,53,55,59,
%T A325461 61,67,71,73,75,77,79,83,89,91,97,101,103,107,109,113,119,121,127,131,
%U A325461 137,139,143,149,151,157,163,167,169,173,179,181,187,191,193,197
%N A325461 Heinz numbers of integer partitions with strictly decreasing differences (with the last part taken to be 0).
%C A325461 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325461 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 A325461 The enumeration of these partitions by sum is given by A320510.
%H A325461 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325461 The sequence of terms together with their prime indices begins:
%e A325461     1: {}
%e A325461     2: {1}
%e A325461     3: {2}
%e A325461     4: {1,1}
%e A325461     5: {3}
%e A325461     7: {4}
%e A325461     9: {2,2}
%e A325461    11: {5}
%e A325461    13: {6}
%e A325461    15: {2,3}
%e A325461    17: {7}
%e A325461    19: {8}
%e A325461    23: {9}
%e A325461    25: {3,3}
%e A325461    29: {10}
%e A325461    31: {11}
%e A325461    35: {3,4}
%e A325461    37: {12}
%e A325461    41: {13}
%e A325461    43: {14}
%t A325461 primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A325461 Select[Range[100],Greater@@Differences[Append[primeptn[#],0]]&]
%Y A325461 Cf. A056239, A112798, A320510, A325327, A325362, A325364, A325367, A325388, A325390, A325396, A325399, A325407, A325457, A325460.
%K A325461 nonn
%O A325461 1,2
%A A325461 _Gus Wiseman_, May 03 2019