A300724 - OEIS

%I #13 Mar 14 2018 03:49:37

%S 1,1,1,2,3,1,3,4,6,3,7,2,7,3,3,8,15,6,15,6,11,7,15,4,12,7,8,6,15,3,15,

%T 16,23,15,25,12,31,15,23,12,31,11,31,14,18,15,31,8,28,12,15,14,31,8,

%U 21,12,15,15,31,6,31,15,10,32,53,23,63,30,47,25,63,24,63,31,44,30,53,23,63,24,48,31,63,22,45,31,47,28,63,18,53,30,47,31

%N Möbius transform of A053644(n), largest power of 2 less than or equal to n.

%H Antti Karttunen, <a href="/A300724/b300724.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = Sum_{d|n} A008683(n/d)*A053644(d).

%F a(n) + A300725(n) = A000010(n).

%o (PARI)

%o A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644

%o A300724(n) = sumdiv(n,d,moebius(n/d)*A053644(d));

%Y Cf. A000010, A053644, A297111, A297115, A300723, A300725, A300726.

%K nonn

%O 1,4

%A _Antti Karttunen_, Mar 11 2018