A324902 - OEIS

%I #10 Jul 01 2022 22:13:27

%S 0,0,0,0,0,1,0,0,0,1,0,2,0,1,0,0,0,0,0,1,0,1,0,2,0,1,0,2,0,1,0,0,0,1,

%T 0,0,0,1,0,1,0,1,0,2,0,1,0,2,0,0,0,1,0,1,0,3,0,1,0,2,0,1,0,0,0,1,0,1,

%U 0,1,0,0,0,1,0,2,0,1,0,1,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,0,0,0,0,1,0,1,0

%N The 2-adic valuation of A318456(n), where A318456(n) = n OR (sigma(n)-n).

%H Antti Karttunen, <a href="/A324902/b324902.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A007814(A318456(n)).

%F a(n) = A324904(n) - A324903(n).

%o (PARI)

%o A318456(n) = bitor(n,sigma(n)-n);

%o A324902(n) = valuation(A318456(n),2);

%o (Python)

%o from sympy import divisor_sigma

%o def A324902(n): return (~(m:=n|int(divisor_sigma(n))-n) & m-1).bit_length() # _Chai Wah Wu_, Jul 01 2022

%Y Cf. A000203, A001065, A003986, A007814, A318456, A324882, A324903, A324904.

%K nonn

%O 1,12

%A _Antti Karttunen_, Mar 28 2019