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A336123 a(1) = 0, a(2) = 1, and for n > 2, a(n) = [A122111(n) == 1 (mod 4)] + a(A253553(n)).

%I A336123 #9 Jul 17 2020 22:58:12
%S A336123 0,1,1,1,1,1,1,2,2,1,1,2,1,1,2,2,1,1,1,2,2,1,1,2,1,1,3,2,1,1,1,2,2,1,
%T A336123 1,3,1,1,2,2,1,1,1,2,3,1,1,2,2,2,2,2,1,1,1,2,2,1,1,3,1,1,3,3,1,1,1,2,
%U A336123 2,2,1,3,1,1,2,2,2,1,1,2,4,1,1,3,1,1,2,2,1,1,2,2,2,1,1,3,1,1,3,2,1,1,1,2,2
%N A336123 a(1) = 0, a(2) = 1, and for n > 2, a(n) = [A122111(n) == 1 (mod 4)] + a(A253553(n)).
%H A336123 Antti Karttunen, <a href="/A336123/b336123.txt">Table of n, a(n) for n = 1..65537</a>
%F A336123 a(1) = 0, a(2) = 1, and for n > 2, a(n) = [A336124(n) == 1] + a(A253553(n)).
%F A336123 a(n) = A000120(A336125(n)).
%F A336123 For n > 1, a(n) = A292375(A122111(n)).
%F A336123 a(n) = A001222(n) - A336121(n).
%F A336123 For all n >= 0, a(3^n) = n.
%o A336123 (PARI)
%o A336123 \\ Uses also code given in A336124:
%o A336123 A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
%o A336123 A336123(n) = if(n<=2,n-1,(1==A336124(n))+A336123(A253553(n)));
%Y A336123 Cf. A000120, A000244, A001222, A122111, A292375, A336121, A336124, A336125.
%K A336123 nonn
%O A336123 1,8
%A A336123 _Antti Karttunen_, Jul 17 2020