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A322027 Maximum order of primeness among the prime factors of n; a(1) = 0.

%I A322027 #11 Nov 28 2018 19:04:23
%S A322027 0,1,2,1,3,2,1,1,2,3,4,2,1,1,3,1,2,2,1,3,2,4,1,2,3,1,2,1,1,3,5,1,4,2,
%T A322027 3,2,1,1,2,3,2,2,1,4,3,1,1,2,1,3,2,1,1,2,4,1,2,1,3,3,1,5,2,1,3,4,2,2,
%U A322027 2,3,1,2,1,1,3,1,4,2,1,3,2,2,2,2,3,1,2
%N A322027 Maximum order of primeness among the prime factors of n; a(1) = 0.
%C A322027 The order of primeness (A078442) of a prime number p is the number of times one must apply A000720 to obtain a nonprime number.
%H A322027 Alois P. Heinz, <a href="/A322027/b322027.txt">Table of n, a(n) for n = 1..65536</a>
%H A322027 N. Fernandez, <a href="http://www.borve.org/primeness/FOP.html">An order of primeness, F(p)</a>
%H A322027 N. Fernandez, <a href="/A006450/a006450.html">An order of primeness</a> [cached copy, included at A006450 with permission of the author]
%e A322027 a(105) = 3 because the prime factor of 105 = 3*5*7 with maximum order of primeness is 5, with order 3.
%p A322027 with(numtheory):
%p A322027 p:= proc(n) option remember;
%p A322027       `if`(isprime(n), 1+p(pi(n)), 0)
%p A322027     end:
%p A322027 a:= n-> max(0, map(p, factorset(n))):
%p A322027 seq(a(n), n=1..120);  # _Alois P. Heinz_, Nov 24 2018
%t A322027 Table[If[n==1,0,Max@@(Length[NestWhileList[PrimePi,PrimePi[#],PrimeQ]]&/@FactorInteger[n][[All,1]])],{n,100}]
%Y A322027 Cf. A000720, A006450, A007097, A007821, A049076, A076610, A078442, A109082, A114537, A184155, A276625, A279065, A322028, A322030.
%K A322027 nonn
%O A322027 1,3
%A A322027 _Gus Wiseman_, Nov 24 2018