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A300725 Möbius transform of A053645(n), distance to the largest power of 2 less than or equal to n.

%I A300725 #16 Mar 24 2018 18:54:38
%S A300725 0,0,1,0,1,1,3,0,0,1,3,2,5,3,5,0,1,0,3,2,1,3,7,4,8,5,10,6,13,5,15,0,
%T A300725 -3,1,-1,0,5,3,1,4,9,1,11,6,6,7,15,8,14,8,17,10,21,10,19,12,21,13,27,
%U A300725 10,29,15,26,0,-5,-3,3,2,-3,-1,7,0,9,5,-4,6,7,1,15,8,6,9,19,2,19,11,9,12,25,6,19,14,13,15,27
%N A300725 Möbius transform of A053645(n), distance to the largest power of 2 less than or equal to n.
%H A300725 Antti Karttunen, <a href="/A300725/b300725.txt">Table of n, a(n) for n = 1..65537</a>
%F A300725 a(n) = Sum_{d|n} A008683(n/d)*A053645(d).
%F A300725 a(n) + A300724(n) = A000010(n).
%t A300725 With[{s = Array[# - 2^Floor@ Log2@ # &, 95]}, Table[DivisorSum[n, MoebiusMu[n/#] s[[#]] &], {n, Length@ s}]] (* _Michael De Vlieger_, Mar 13 2018 *)
%o A300725 (PARI)
%o A300725 A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644
%o A300725 A053645(n) = (n-A053644(n));
%o A300725 A300725(n) = sumdiv(n,d,moebius(n/d)*A053645(d));
%Y A300725 Cf. A000010, A008683, A053644, A053645, A297111, A297115, A300723, A300724.
%K A300725 sign,look
%O A300725 1,7
%A A300725 _Antti Karttunen_, Mar 11 2018