A323014 - OEIS

%I #13 Jun 12 2022 15:39:38

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

%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 (A101296, A118914) of the index.

%H Antti Karttunen, <a href="/A323014/b323014.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F For all n >= 1, a(n) = a(A046523(n)). [See comment] - _Antti Karttunen_, Jun 10 2022

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

%t Array[dep,100]

%o (PARI)

%o A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));

%o A323014(n) = if(1==n,0,if(isprime(n),1, 1+A323014(A181819(n)))); \\ _Antti Karttunen_, Jun 10 2022

%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, A046523, A056239, A070175, A071625, A101296, A112798, A118914, A181819, A181821, A182850, A182857, A304465, A323022.

%K nonn

%O 1,4

%A _Gus Wiseman_, Jan 02 2019

%E Terms a(88) and beyond from _Antti Karttunen_, Jun 10 2022