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A325367 Heinz numbers of integer partitions with distinct differences between successive parts (with the last part taken to be zero). 17

%I

%S 1,2,3,4,5,7,9,10,11,13,14,15,17,19,20,22,23,25,26,28,29,31,33,34,35,

%T 37,38,39,41,43,44,45,46,47,49,50,51,52,53,55,57,58,59,61,62,67,68,69,

%U 71,73,74,75,76,77,79,82,83,85,86,87,89,91,92,93,94,95,97

%N Heinz numbers of integer partitions with distinct differences between successive parts (with the last part taken to be zero).

%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 A325324.

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

%e The sequence of terms together with their prime indices begins:

%e 1: {}

%e 2: {1}

%e 3: {2}

%e 4: {1,1}

%e 5: {3}

%e 7: {4}

%e 9: {2,2}

%e 10: {1,3}

%e 11: {5}

%e 13: {6}

%e 14: {1,4}

%e 15: {2,3}

%e 17: {7}

%e 19: {8}

%e 20: {1,1,3}

%e 22: {1,5}

%e 23: {9}

%e 25: {3,3}

%e 26: {1,6}

%e 28: {1,1,4}

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

%t Select[Range[200],UnsameQ@@Differences[Append[primeptn[#],0]]&]

%Y Positions of squarefree numbers in A325390.

%Y Cf. A056239, A112798, A130091, A320348, A325324, A325327, A325362, A325364, A325366, A325368, A325388, A325405, A325407, A325460, A325461.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 02 2019

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Last modified January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)