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%I #9 May 21 2022 19:40:10
%S 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,
%T 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,
%U 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
%N Number of runs in the ordered prime signature of n.
%C First differs from A071625 at a(90) = 3.
%C First differs from A331592 at a(90) = 3.
%C A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.
%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/q/87559">What is a sequence run? (answered 2011-12-01)</a>
%e 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.
%t Table[Length[Split[Last/@If[n==1,{},FactorInteger[n]]]],{n,100}]
%Y Positions of first appearances are A354233.
%Y A001222 counts prime factors, distinct A001221.
%Y A005361 gives product of prime signature, firsts A353500/A085629.
%Y A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A124010 gives prime signature, sorted A118914.
%Y A181819 gives prime shadow, with an inverse A181821.
%Y A182850/A323014 give frequency depth, counted by A225485/A325280.
%Y Cf. A005811, A097318, A130091, A304678, A333755, A353503, A353507, A353742.
%K nonn
%O 1,12
%A _Gus Wiseman_, May 20 2022
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