cp's OEIS Frontend

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

%I A347380 #11 Jan 30 2022 09:51:02
%S A347380 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 A347380 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 A347380 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 A347380 Length of the common prefix in the binary expansions of A156552(n) and A332221(n) = A156552(sigma(n)).
%H A347380 Antti Karttunen, <a href="/A347380/b347380.txt">Table of n, a(n) for n = 1..20000</a>
%H A347380 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A347380 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A347380 a(n) = A252464(n) - A347381(n).
%F A347380 a(n) = A348040(n, A000203(n)). - _Antti Karttunen_, Jan 30 2022
%o A347380 (PARI)
%o A347380 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 A347380 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 A347380(n) = Abincompreflen(A156552(n), A156552(sigma(n)));
%Y A347380 Cf. A000203, A156552, A252464, A332221, A347381, A348040.
%K A347380 nonn
%O A347380 1,5
%A A347380 _Antti Karttunen_, Aug 30 2021