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A324734 Number of 0-bits present between the most and the least significant 1-bits in A324712(n), and 0 if A324712(n) = 0; a(n) = A324733(n) - A324829(n).

%I A324734 #8 Mar 17 2019 21:07:53
%S A324734 0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,2,1,0,0,1,2,1,2,0,0,0,0,2,2,
%T A324734 3,1,0,0,2,0,0,0,0,3,2,2,0,0,2,2,0,3,0,0,4,1,2,2,0,1,0,4,1,2,3,1,0,5,
%U A324734 2,1,0,1,0,2,3,2,3,1,0,0,1,5,0,1,3,3,4,1,0,1,2,5,4,5,3,0,0,0,4,2,0,4,0,0,1
%N A324734 Number of 0-bits present between the most and the least significant 1-bits in A324712(n), and 0 if A324712(n) = 0; a(n) = A324733(n) - A324829(n).
%H A324734 Antti Karttunen, <a href="/A324734/b324734.txt">Table of n, a(n) for n = 1..10000</a>
%H A324734 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324734 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A324734 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A324734 a(n) = A324733(n) - A324829(n).
%F A324734 a(p) = 0 for all primes p.
%o A324734 (PARI)
%o A324734 A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v,
%o A324734 A323243(d)))); (v); }; \\ Needs also code from A323243.
%o A324734 A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523
%o A324734 A007814(n) = valuation(n,2)
%o A324734 A324829(n) = hammingweight(A324712(n));
%o A324734 A324733(n) = { my(k=A324712(n)); if(!k,k,1 + (A000523(k)-A007814(k))); };
%o A324734 A324734(n) = (A324733(n) - A324829(n));
%Y A324734 Cf. A323243, A324712, A324733, A324829, A324735.
%K A324734 nonn
%O A324734 1,21
%A A324734 _Antti Karttunen_, Mar 17 2019