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A358170
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Heinz number of the partial sums of the n-th composition in standard order (A066099).
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6
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1, 2, 3, 6, 5, 15, 10, 30, 7, 35, 21, 105, 14, 70, 42, 210, 11, 77, 55, 385, 33, 231, 165, 1155, 22, 154, 110, 770, 66, 462, 330, 2310, 13, 143, 91, 1001, 65, 715, 455, 5005, 39, 429, 273, 3003, 195, 2145, 1365, 15015, 26, 286, 182, 2002, 130, 1430, 910, 10010
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OFFSET
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0,2
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COMMENTS
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The k-th composition in standard order (graded reverse-lexicographic, 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. This gives a bijective correspondence between nonnegative integers and integer compositions.
The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
1: {}
2: {1}
3: {2}
6: {1,2}
5: {3}
15: {2,3}
10: {1,3}
30: {1,2,3}
7: {4}
35: {3,4}
21: {2,4}
105: {2,3,4}
14: {1,4}
70: {1,3,4}
42: {1,2,4}
210: {1,2,3,4}
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MATHEMATICA
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stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Times@@Prime/@#&/@Table[Accumulate[stc[n]], {n, 0, 100}]
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CROSSREFS
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See link for sequences related to standard compositions.
The image is A005117 (squarefree numbers).
Least prime index of a(n) is A065120.
These are the Heinz numbers of the rows of A358134.
Sum of prime indices of a(n) is A359042.
A066099 lists standard compositions.
Cf. A000720, A001511, A029931, A059893, A061395, A241916, A242628, A355536, A358133, A358135, A358137.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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