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%I #8 Mar 17 2020 21:18:10
%S 1,2,3,4,5,6,6,8,7,10,9,12,10,12,12,16,11,14,15,20,15,18,18,24,14,20,
%T 18,24,20,24,24,32,13,22,21,28,25,30,30,40,21,30,27,36,30,36,36,48,22,
%U 28,30,40,30,36,36,48,28,40,36,48,40,48,48,64,17,26,33,44
%N Heinz number of the n-th composition in standard order.
%C Includes all positive integers.
%C The k-th composition in standard order (row k of A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again.
%C The Heinz number of a composition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%F A056239(a(n)) = A070939(n).
%e The sequence of terms together with their prime indices begins:
%e 1: {} 15: {2,3} 25: {3,3}
%e 2: {1} 20: {1,1,3} 30: {1,2,3}
%e 3: {2} 15: {2,3} 30: {1,2,3}
%e 4: {1,1} 18: {1,2,2} 40: {1,1,1,3}
%e 5: {3} 18: {1,2,2} 21: {2,4}
%e 6: {1,2} 24: {1,1,1,2} 30: {1,2,3}
%e 6: {1,2} 14: {1,4} 27: {2,2,2}
%e 8: {1,1,1} 20: {1,1,3} 36: {1,1,2,2}
%e 7: {4} 18: {1,2,2} 30: {1,2,3}
%e 10: {1,3} 24: {1,1,1,2} 36: {1,1,2,2}
%e 9: {2,2} 20: {1,1,3} 36: {1,1,2,2}
%e 12: {1,1,2} 24: {1,1,1,2} 48: {1,1,1,1,2}
%e 10: {1,3} 24: {1,1,1,2} 22: {1,5}
%e 12: {1,1,2} 32: {1,1,1,1,1} 28: {1,1,4}
%e 12: {1,1,2} 13: {6} 30: {1,2,3}
%e 16: {1,1,1,1} 22: {1,5} 40: {1,1,1,3}
%e 11: {5} 21: {2,4} 30: {1,2,3}
%e 14: {1,4} 28: {1,1,4} 36: {1,1,2,2}
%t stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t Table[Times@@Prime/@stc[n],{n,0,100}]
%Y The length of the k-th composition in standard order is A000120(k).
%Y The sum of the k-th composition in standard order is A070939(k).
%Y The maximum of the k-th composition in standard order is A070939(k).
%Y A partial inverse is A333220. See also A233249.
%Y Cf. A048793, A056239, A066099, A112798, A114994, A124767, A213925, A225620, A228351, A233564, A272919, A333218.
%K nonn
%O 1,2
%A _Gus Wiseman_, Mar 16 2020
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