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A353745
Number of runs in the ordered prime signature of n.
2
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1
OFFSET
1,12
COMMENTS
First differs from A071625 at a(90) = 3.
First differs from A331592 at a(90) = 3.
A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.
EXAMPLE
The prime indices of 630 are {1,2,2,3,4}, with multiplicities {1,2,1,1}, with runs {{1},{2},{1,1}}, so a(630) = 3.
MATHEMATICA
Table[Length[Split[Last/@If[n==1, {}, FactorInteger[n]]]], {n, 100}]
CROSSREFS
Positions of first appearances are A354233.
A001222 counts prime factors, distinct A001221.
A005361 gives product of prime signature, firsts A353500/A085629.
A056239 adds up prime indices, row sums of A112798 and A296150.
A124010 gives prime signature, sorted A118914.
A181819 gives prime shadow, with an inverse A181821.
A182850/A323014 give frequency depth, counted by A225485/A325280.
Sequence in context: A003652 A071625 A331592 * A309004 A355382 A304779
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 20 2022
STATUS
approved