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

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, 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, 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

Offset

1,4

Comments

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences computed from exponents in factorization of n

Formula

For all n >= 1, a(n) = a(A046523(n)). [See comment] - Antti Karttunen, Jun 10 2022

Mathematica

dep[n_]:=If[n==1, 0, If[PrimeQ[n], 1, 1+dep[Times@@Prime/@Last/@FactorInteger[n]]]];
Array[dep, 100]

Prog

(PARI)
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
A323014(n) = if(1==n, 0, if(isprime(n), 1, 1+A323014(A181819(n)))); \\ Antti Karttunen, Jun 10 2022

Crossrefs

Positions of 1's are the prime numbers A000040.

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

Positions of 3's are A182853.

Row lengths of A323023.

Cf. A001221, A001222, A046523, A056239, A070175, A071625, A101296, A112798, A118914, A181819, A181821, A182850, A182857, A304465, A323022.

Sequence in context: A305818 A303757 A182850 * A350331 A293227 A291208

Adjacent sequences: A323011 A323012 A323013 * A323015 A323016 A323017

Keyword

nonn

Author

Gus Wiseman, Jan 02 2019

Extensions

Terms a(88) and beyond from Antti Karttunen, Jun 10 2022

Status

approved