A336921 - OEIS

%I #10 Aug 10 2020 00:19:48

%S 0,0,0,0,1,0,0,0,0,1,1,0,1,0,1,0,2,0,2,1,0,1,1,0,2,1,0,0,3,1,0,0,1,2,

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

%U 1,1,2,0,4,3,2,2,1,1,2,1,0,2,2,0,3,2,3,1,4,1,1,1,0,1,3,0,2,0,1,2,4,2,2,1,1

%N a(n) = A331410(n) - A087436(n).

%C Totally additive because both A087436 and A331410 are.

%H Antti Karttunen, <a href="/A336921/b336921.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A331410(A336467(n)).

%F a(n) = A331410(n) - A087436(n).

%F a(n) = A336922(n) - A046660(A000265(n)).

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

%o (PARI)

%o A000265(n) = (n>>valuation(n,2));

%o A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));

%o A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };

%o A336921(n) = A331410(A336467(n));

%Y Cf. A000265, A046660, A087436, A331410, A336467, A336922.

%Y Cf. also A336118, A336396.

%K nonn

%O 1,17

%A _Antti Karttunen_, Aug 09 2020