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A300726 Difference between A053644 (the largest power of 2 less than or equal to n) and its Möbius transform.

%I A300726 #12 Mar 24 2018 18:54:50
%S A300726 0,1,1,2,1,3,1,4,2,5,1,6,1,5,5,8,1,10,1,10,5,9,1,12,4,9,8,10,1,13,1,
%T A300726 16,9,17,7,20,1,17,9,20,1,21,1,18,14,17,1,24,4,20,17,18,1,24,11,20,17,
%U A300726 17,1,26,1,17,22,32,11,41,1,34,17,39,1,40,1,33,20,34,11,41,1,40,16,33,1,42,19,33,17,36,1,46,11,34,17,33,19
%N A300726 Difference between A053644 (the largest power of 2 less than or equal to n) and its Möbius transform.
%H A300726 Antti Karttunen, <a href="/A300726/b300726.txt">Table of n, a(n) for n = 1..65537</a>
%F A300726 a(n) = -Sum_{d|n, d<n} A008683(n/d)*A053644(d).
%F A300726 a(n) = A053644(n) - A300724(n).
%t A300726 With[{s = Array[2^Floor@ Log2@ # &, 95]}, Table[s[[n]] - DivisorSum[n, MoebiusMu[n/#] s[[#]] &], {n, Length@ s}]] (* _Michael De Vlieger_, Mar 13 2018 *)
%o A300726 (PARI)
%o A300726 A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644
%o A300726 A300726(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A053644(d));
%Y A300726 Cf. A008683, A053644, A300724, A300725, A300244.
%K A300726 nonn,look
%O A300726 1,4
%A A300726 _Antti Karttunen_, Mar 11 2018