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A336921 a(n) = A331410(n) - A087436(n).

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%I A336921 #10 Aug 10 2020 00:19:48
%S A336921 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 A336921 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 A336921 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 A336921 a(n) = A331410(n) - A087436(n).
%C A336921 Totally additive because both A087436 and A331410 are.
%H A336921 Antti Karttunen, <a href="/A336921/b336921.txt">Table of n, a(n) for n = 1..65537</a>
%F A336921 a(n) = A331410(A336467(n)).
%F A336921 a(n) = A331410(n) - A087436(n).
%F A336921 a(n) = A336922(n) - A046660(A000265(n)).
%F A336921 For all n >= 1, a(n) <= A336118(n).
%o A336921 (PARI)
%o A336921 A000265(n) = (n>>valuation(n,2));
%o A336921 A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
%o A336921 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 A336921(n) = A331410(A336467(n));
%Y A336921 Cf. A000265, A046660, A087436, A331410, A336467, A336922.
%Y A336921 Cf. also A336118, A336396.
%K A336921 nonn
%O A336921 1,17
%A A336921 _Antti Karttunen_, Aug 09 2020