A325368 - OEIS

%I #4 May 02 2019 16:04:56

%S 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 31,33,34,35,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,55,57,58,59,

%U 61,62,63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,82,83

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

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%C The enumeration of these partitions by sum is given by A325325.

%H Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>

%e Most small numbers are in the sequence, but the sequence of non-terms together with their prime indices begins:

%e     8: {1,1,1}

%e    16: {1,1,1,1}

%e    24: {1,1,1,2}

%e    27: {2,2,2}

%e    30: {1,2,3}

%e    32: {1,1,1,1,1}

%e    36: {1,1,2,2}

%e    40: {1,1,1,3}

%e    48: {1,1,1,1,2}

%e    54: {1,2,2,2}

%e    56: {1,1,1,4}

%e    60: {1,1,2,3}

%e    64: {1,1,1,1,1,1}

%e    72: {1,1,1,2,2}

%e    80: {1,1,1,1,3}

%e    81: {2,2,2,2}

%e    88: {1,1,1,5}

%e    90: {1,2,2,3}

%e    96: {1,1,1,1,1,2}

%e   100: {1,1,3,3}

%t primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];

%t Select[Range[100],UnsameQ@@Differences[primeptn[#]]&]

%Y Cf. A056239, A112798, A130091, A240026, A325325, A325328, A325352, A325360, A325361, A325366, A325367, A325405, A325456, A325457.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 02 2019