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A323014 a(1) = 0; a(prime) = 1; otherwise a(n) = 1 + a(A181819(n)). 75

%I

%S 0,1,1,2,1,3,1,2,2,3,1,4,1,3,3,2,1,4,1,4,3,3,1,4,2,3,2,4,1,3,1,2,3,3,

%T 3,3,1,3,3,4,1,3,1,4,4,3,1,4,2,4,3,4,1,4,3,4,3,3,1,5,1,3,4,2,3,3,1,4,

%U 3,3,1,4,1,3,4,4,3,3,1,4,2,3,1,5,3,3,3

%N a(1) = 0; a(prime) = 1; otherwise a(n) = 1 + a(A181819(n)).

%C Except for n = 2, same as A182850. Unlike A182850, the terms of this sequence depend only on the prime signature (A118914) of the index.

%t dep[n_]:=If[n==1,0,If[PrimeQ[n],1,1+dep[Times@@Prime/@Last/@FactorInteger[n]]]];

%t Array[dep,100]

%Y Positions of 1's are the prime numbers A000040.

%Y Positions of 2's are the proper prime powers A246547.

%Y Positions of 3's are A182853.

%Y Row lengths of A323023.

%Y Cf. A001221, A001222, A056239, A070175, A071625, A112798, A118914, A181819, A181821, A182850, A182857, A304465, A323022.

%K nonn

%O 1,4

%A _Gus Wiseman_, Jan 02 2019

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Last modified January 29 14:07 EST 2020. Contains 331338 sequences. (Running on oeis4.)