A364955 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)).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Sep 02 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

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

Cf. also A364570.

Programs

PARI

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); };
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
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));
A364954(n) = Abincompreflen(A156552(n), A156552(A163511(n)));
A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
A252464(n) = if(1==n,0,(bigomega(n) + A061395(n) - 1));
A364955(n) = (A252464(n)-A364954(n));