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A324728 Binary length of A324712: a(n) = 0 if A324712(n) = 0, otherwise a(n) = 1+A000523(A324712(n)).

%I A324728 #7 Mar 17 2019 21:07:14
%S A324728 0,1,2,3,3,3,4,4,4,4,5,4,6,5,5,5,7,3,8,5,6,6,9,5,5,7,5,6,10,6,11,6,6,
%T A324728 8,6,6,12,9,8,6,13,5,14,7,6,10,15,6,6,4,8,8,16,3,7,7,10,11,17,5,18,12,
%U A324728 5,7,7,7,19,9,10,5,20,7,21,13,6,10,7,7,22,7,7,14,23,7,9,15,12,8,24,7,8,11,12,16,10,7,25,5,8,7,26,9,27,9,7
%N A324728 Binary length of A324712: a(n) = 0 if A324712(n) = 0, otherwise a(n) = 1+A000523(A324712(n)).
%H A324728 Antti Karttunen, <a href="/A324728/b324728.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)
%H A324728 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324728 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A324728 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324728 If A324712(n) = 0, then a(n) = 0, otherwise a(n) = 1+A000523(A324712(n)).
%F A324728 a(A000040(n)) = n.
%o A324728 (PARI)
%o A324728 A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A323243(d)))); (v); }; \\ Needs also code from A323243.
%o A324728 A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523
%o A324728 A324728(n) = { my(k=A324712(n)); if(!k,k,(1+A000523(k))); };
%Y A324728 Cf. A000523, A323243, A324712, A324733, A324735, A324811.
%K A324728 nonn
%O A324728 1,3
%A A324728 _Antti Karttunen_, Mar 17 2019