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A325390 Heinz number of the negated differences plus one of the integer partition with Heinz number n (with the last part taken to be 0).

%I A325390 #5 May 03 2019 08:35:51
%S A325390 1,3,5,6,7,9,11,12,10,15,13,18,17,21,15,24,19,18,23,30,25,33,29,36,14,
%T A325390 39,20,42,31,27,37,48,35,51,21,36,41,57,55,60,43,45,47,66,30,69,53,72,
%U A325390 22,30,65,78,59,36,35,84,85,87,61,54,67,93,50,96,49,63,71
%N A325390 Heinz number of the negated differences plus one of the integer partition with Heinz number n (with the last part taken to be 0).
%C A325390 The Heinz number of a positive integer sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325390 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).
%H A325390 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325390 The Heinz number of (6,3,1) is 130, and its negated differences plus one are (4,3,2), which has Heinz number 105, so a(130) = 105.
%t A325390 primeptn[n_]:=If[n==1,{},Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A325390 Table[Times@@Prime/@(1-Differences[Append[primeptn[n],0]]),{n,100}]
%Y A325390 Number of appearances of n is A325392(n).
%Y A325390 Positions of squarefree numbers are A325367.
%Y A325390 Cf. A007294, A007862, A056239, A112798, A320509, A325324, A325327, A325351, A325352, A325362, A325364, A325460, A325461.
%K A325390 nonn
%O A325390 1,2
%A A325390 _Gus Wiseman_, May 02 2019