A324733 - OEIS

%I #8 Mar 17 2019 21:07:45

%S 0,1,2,3,3,1,4,2,4,4,5,4,6,3,4,1,7,3,8,3,6,5,9,2,5,6,3,6,10,4,11,3,5,

%T 7,5,4,12,7,6,1,13,2,14,7,6,9,15,3,6,4,1,8,16,1,7,5,8,8,17,4,18,11,3,

%U 4,6,7,19,9,9,4,20,5,21,12,6,10,6,7,22,4,3,13,23,7,6,14,10,5,24,7,8,11,11,15,8,3,25,2,8,6,26,9,27,2,5

%N a(n) = 0 if A324712(n) = 0, otherwise a(n) = 1 + A000523(A324712(n)) - A007814(A324712(n)).

%H Antti Karttunen, <a href="/A324733/b324733.txt">Table of n, a(n) for n = 1..10000</a> (based on Hans Havermann's factorization of A156552)

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F If A324712(n) = 0, then a(n) = 0, otherwise a(n) = 1 + A324728(n) - A324724(n).

%o (PARI)

%o A324712(n) = { my(v=0); fordiv(n, d, if(issquarefree(n/d), v=bitxor(v, A323243(d)))); (v); }; \\ Needs also code from A323243.

%o A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523

%o A007814(n) = valuation(n,2)

%o A324733(n) = { my(k=A324712(n)); if(!k,k,1 + (A000523(k)-A007814(k))); };

%Y Cf. A323243, A324712, A324724, A324728, A324734, A324735.

%K nonn

%O 1,3

%A _Antti Karttunen_, Mar 17 2019