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A353838
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Numbers whose prime indices have all distinct run-sums.
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36
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71
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OFFSET
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1,2
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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.
The sequence of runs of a sequence consists of its maximal consecutive constant subsequences when read left-to-right. 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 180 are {1,1,2,2,3}, with run-sums (2,4,3), so 180 is in the sequence.
The prime indices of 315 are {2,2,3,4}, with run-sums (4,3,4), so 315 is not in the sequence.
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MATHEMATICA
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Select[Range[100], UnsameQ@@Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]&]
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CROSSREFS
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These partitions are counted by A353837.
A098859 counts partitions with distinct multiplicities, ranked by A130091.
A165413 counts distinct run-sums in binary expansion.
A351014 counts distinct runs in standard compositions.
A353832 represents taking run-sums of a partition, compositions A353847.
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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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