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A353833
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Numbers whose multiset of prime indices has all equal run-sums.
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33
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1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 40, 41, 43, 47, 49, 53, 59, 61, 63, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 112, 113, 121, 125, 127, 128, 131, 137, 139, 144, 149, 151, 157, 163, 167, 169, 173, 179
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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 12 are {1,1,2}, with run-sums (2,2), so 12 is in the sequence.
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MATHEMATICA
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Select[Range[100], SameQ@@Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]*k]&]
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CROSSREFS
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For run-lengths instead of run-sums we have A072774, counted by A047966.
These partitions are counted by A304442.
These are the positions of powers of primes in A353832.
The restriction to nonprimes is A353834.
For distinct instead of equal run-sums we have A353838, counted by A353837.
A005811 counts runs in binary expansion, distinct run-lengths A165413.
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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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