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A325368 Heinz numbers of integer partitions with distinct differences between successive parts.

%I A325368 #4 May 02 2019 16:04:56
%S A325368 1,2,3,4,5,6,7,9,10,11,12,13,14,15,17,18,19,20,21,22,23,25,26,28,29,
%T A325368 31,33,34,35,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,55,57,58,59,
%U A325368 61,62,63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,82,83
%N A325368 Heinz numbers of integer partitions with distinct differences between successive parts.
%C A325368 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325368 The enumeration of these partitions by sum is given by A325325.
%H A325368 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325368 Most small numbers are in the sequence, but the sequence of non-terms together with their prime indices begins:
%e A325368     8: {1,1,1}
%e A325368    16: {1,1,1,1}
%e A325368    24: {1,1,1,2}
%e A325368    27: {2,2,2}
%e A325368    30: {1,2,3}
%e A325368    32: {1,1,1,1,1}
%e A325368    36: {1,1,2,2}
%e A325368    40: {1,1,1,3}
%e A325368    48: {1,1,1,1,2}
%e A325368    54: {1,2,2,2}
%e A325368    56: {1,1,1,4}
%e A325368    60: {1,1,2,3}
%e A325368    64: {1,1,1,1,1,1}
%e A325368    72: {1,1,1,2,2}
%e A325368    80: {1,1,1,1,3}
%e A325368    81: {2,2,2,2}
%e A325368    88: {1,1,1,5}
%e A325368    90: {1,2,2,3}
%e A325368    96: {1,1,1,1,1,2}
%e A325368   100: {1,1,3,3}
%t A325368 primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A325368 Select[Range[100],UnsameQ@@Differences[primeptn[#]]&]
%Y A325368 Cf. A056239, A112798, A130091, A240026, A325325, A325328, A325352, A325360, A325361, A325366, A325367, A325405, A325456, A325457.
%K A325368 nonn
%O A325368 1,2
%A A325368 _Gus Wiseman_, May 02 2019