A347380 Length of the common prefix in the binary expansions of A156552(n) and A332221(n) = A156552(sigma(n)).

0, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 2, 4, 2, 3, 1, 1, 1, 3, 4, 1, 1, 2, 3, 1, 3, 1, 6, 2, 1, 1, 1, 2, 1, 3, 1, 8, 2, 4, 2, 3, 2, 5, 3, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 11, 2, 3, 1, 3, 1, 7, 3, 2, 1, 1, 1, 12, 7, 1, 2, 3, 3, 3, 3, 2, 3, 3, 3, 1, 4, 2, 2, 2, 2, 3, 3, 1, 1, 2, 2, 1, 1, 4, 1, 6, 1, 6, 2, 3

Offset: 1

Author

Antti Karttunen, Aug 30 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A156552, A252464, A332221, A347381, A348040.

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
A347380(n) = Abincompreflen(A156552(n), A156552(sigma(n)));

Formula

a(n) = A252464(n) - A347381(n).

a(n) = A348040(n, A000203(n)). - Antti Karttunen, Jan 30 2022