%I #9 Sep 02 2023 16:59:56

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

%T 4,3,11,8,6,5,12,5,13,6,4,9,14,0,4,4,6,6,14,4,4,4,6,8,14,4,14,7,3,0,6,

%U 6,18,8,9,5,19,4,20,12,3,9,5,7,21,6,3,13,22,6,7,14,10,7,23,5,6,10,11,15,8,0,23,5,5,5

%N a(n) = A252464(n) - A364954(n), where A364954(n) is the length of the common prefix in the binary expansions of A156552(n) and A156552(A163511(n)).

%H Antti Karttunen, <a href="/A364955/b364955.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%o Abincompreflen(n, m) = { my(x=binary(n), y=binary(m), u=min(#x, #y)); for(i=1, u, if(x[i]!=y[i], return(i-1))); (u); };

%o A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552

%o A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));

%o A364954(n) = Abincompreflen(A156552(n), A156552(A163511(n)));

%o A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);

%o A252464(n) = if(1==n,0,(bigomega(n) + A061395(n) - 1));

%o A364955(n) = (A252464(n)-A364954(n));

%Y Cf. A156552, A163511, A364954, A364956 (positions of 0's).

%Y Cf. also A364570.

%K nonn

%O 1,5

%A _Antti Karttunen_, Sep 02 2023