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A353862
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Greatest run-sum of the prime indices of n.
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11
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0, 1, 2, 2, 3, 2, 4, 3, 4, 3, 5, 2, 6, 4, 3, 4, 7, 4, 8, 3, 4, 5, 9, 3, 6, 6, 6, 4, 10, 3, 11, 5, 5, 7, 4, 4, 12, 8, 6, 3, 13, 4, 14, 5, 4, 9, 15, 4, 8, 6, 7, 6, 16, 6, 5, 4, 8, 10, 17, 3, 18, 11, 4, 6, 6, 5, 19, 7, 9, 4, 20, 4, 21, 12, 6, 8, 5, 6, 22, 4, 8
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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.
A run-sum of a sequence is the sum of any maximal consecutive constant subsequence.
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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) = 4.
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MATHEMATICA
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Table[Max@@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 A051903.
The least run-sum is given by A353931.
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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