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A353931
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Least run-sum of the prime indices of n.
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13
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0, 1, 2, 2, 3, 1, 4, 3, 4, 1, 5, 2, 6, 1, 2, 4, 7, 1, 8, 2, 2, 1, 9, 2, 6, 1, 6, 2, 10, 1, 11, 5, 2, 1, 3, 2, 12, 1, 2, 3, 13, 1, 14, 2, 3, 1, 15, 2, 8, 1, 2, 2, 16, 1, 3, 3, 2, 1, 17, 2, 18, 1, 4, 6, 3, 1, 19, 2, 2, 1, 20, 3, 21, 1, 2, 2, 4, 1, 22, 3, 8, 1
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OFFSET
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1,3
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
Every sequence can be uniquely split into a sequence of non-overlapping runs. For example, the runs of (2,2,1,1,1,3,2,2) are ((2,2),(1,1,1),(3),(2,2)), with sums (4,3,3,4).
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LINKS
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EXAMPLE
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The prime indices of 72 are {1,1,1,2,2}, with run-sums {3,4}, so a(72) = 3.
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MATHEMATICA
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Table[Min@@Cases[FactorInteger[n], {p_, k_}:>PrimePi[p]*k], {n, 100}]
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CROSSREFS
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Positions of first appearances are A008578.
For run-lengths instead of run-sums we have A051904, greatest A051903.
For run-lengths and binary expansion we have A175597, greatest A043276.
The greatest run-sum is given by A353862.
A005811 counts runs in binary expansion.
A304442 counts partitions with all equal run-sums, compositions A353851.
A353832 represents the operation of taking run-sums of a partition.
A353838 ranks partitions with all distinct run-sums, counted by A353837.
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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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