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A305439 a(n) = A046645(n) - A007949(n); the 2-adic valuation of A317932.

%I A305439 #6 Sep 02 2018 17:07:05
%S A305439 0,1,0,3,1,1,1,4,1,2,1,3,1,2,1,7,1,2,1,4,1,2,1,4,3,2,1,4,1,2,1,8,1,2,
%T A305439 2,4,1,2,1,5,1,2,1,4,2,2,1,7,3,4,1,4,1,2,2,5,1,2,1,4,1,2,2,10,2,2,1,4,
%U A305439 1,3,1,5,1,2,3,4,2,2,1,8,3,2,1,4,2,2,1,5,1,3,2,4,1,2,2,8,1,4,2,6,1,2,1,5,2
%N A305439 a(n) = A046645(n) - A007949(n); the 2-adic valuation of A317932.
%C A305439 Apart from a(1) and a(3), all other terms are positive.
%H A305439 Antti Karttunen, <a href="/A305439/b305439.txt">Table of n, a(n) for n = 1..65537</a>
%F A305439 a(n) = A046645(n) - A007949(n).
%F A305439 a(n) = A007814(A317932(n)).
%o A305439 (PARI)
%o A305439 A007949(n) = valuation(n,3);
%o A305439 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A305439 A046645(n) = vecsum(apply(e -> A005187(e),factor(n)[,2]));
%o A305439 A305439(n) = A046645(n) - A007949(n);
%Y A305439 Cf. A007814, A007949, A046645, A317932.
%Y A305439 Cf. also A318440.
%K A305439 nonn
%O A305439 1,4
%A A305439 _Antti Karttunen_, Sep 02 2018