A336396 - OEIS

%I #9 Jul 25 2020 10:34:25

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

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

%U 2,1,3,0,2,2,0,2,2,1,3,0,0,1,2,1,0,3,2,1,2,0,2,2,2,3,2,0,1,2,1,0,2,0,2,1,1

%N a(n) = A329697(n) - A087436(n).

%C Totally additive because both A087436 and A329697 are.

%H Antti Karttunen, <a href="/A336396/b336396.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A329697(n) - A087436(n).

%F a(n) = A329697(A336466(n)).

%F a(n) = A336469(n) - A046660(A000265(n)).

%F For all n >= 1, a(n) <= A336118(n).

%o (PARI)

%o A087436(n) = (bigomega(n>>valuation(n,2)));

%o A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));

%o A336396(n) = (A329697(n) - A087436(n));

%Y Cf. A000265, A046660, A087436, A329697, A336118, A336466, A336469.

%K nonn

%O 1,19

%A _Antti Karttunen_, Jul 24 2020