A347380 - OEIS

%I #11 Jan 30 2022 09:51:02

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A347380/b347380.txt">Table of n, a(n) for n = 1..20000</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 a(n) = A252464(n) - A347381(n).

%F a(n) = A348040(n, A000203(n)). - _Antti Karttunen_, Jan 30 2022

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

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

%K nonn

%O 1,5

%A _Antti Karttunen_, Aug 30 2021