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A325388 Heinz numbers of strict integer partitions with distinct differences (with the last part taken to be 0).

%I A325388 #6 May 03 2019 08:35:34
%S A325388 1,2,3,5,7,10,11,13,14,15,17,19,22,23,26,29,31,33,34,35,37,38,39,41,
%T A325388 43,46,47,51,53,55,57,58,59,61,62,67,69,71,73,74,77,79,82,83,85,86,87,
%U A325388 89,91,93,94,95,97,101,103,106,107,109,111,113,115,118,119,122
%N A325388 Heinz numbers of strict integer partitions with distinct differences (with the last part taken to be 0).
%C A325388 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325388 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 A325388 The enumeration of these partitions by sum is given by A320348.
%H A325388 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325388 The sequence of terms together with their prime indices begins:
%e A325388     1: {}
%e A325388     2: {1}
%e A325388     3: {2}
%e A325388     5: {3}
%e A325388     7: {4}
%e A325388    10: {1,3}
%e A325388    11: {5}
%e A325388    13: {6}
%e A325388    14: {1,4}
%e A325388    15: {2,3}
%e A325388    17: {7}
%e A325388    19: {8}
%e A325388    22: {1,5}
%e A325388    23: {9}
%e A325388    26: {1,6}
%e A325388    29: {10}
%e A325388    31: {11}
%e A325388    33: {2,5}
%e A325388    34: {1,7}
%e A325388    35: {3,4}
%t A325388 primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A325388 Select[Range[100],SquareFreeQ[#]&&UnsameQ@@Differences[Append[primeptn[#],0]]&]
%Y A325388 A subsequence of A005117.
%Y A325388 Cf. A056239, A112798, A320348, A325324, A325327, A325362, A325364, A325366, A325367, A325368, A325390, A325405, A325460, A325461, A325467.
%K A325388 nonn
%O A325388 1,2
%A A325388 _Gus Wiseman_, May 02 2019