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A297115 Möbius transform of A000120, binary weight of n. 9

%I #8 Dec 26 2017 21:25:02

%S 1,0,1,0,1,0,2,0,0,0,2,0,2,0,1,0,1,0,2,0,-1,0,3,0,1,0,2,0,3,0,4,0,-2,

%T 0,-1,0,2,0,0,0,2,0,3,0,0,0,4,0,0,0,1,0,3,0,1,0,0,0,4,0,4,0,3,0,-2,0,

%U 2,0,-2,0,3,0,2,0,-1,0,-1,0,4,0,-1,0,3,0,1,0,0,0,3,0,0,0,-1,0,2,0,2,0,2,0,3,0,4,0,0

%N Möbius transform of A000120, binary weight of n.

%H Antti Karttunen, <a href="/A297115/b297115.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) = Sum_{d|n} A008683(n/d)*A000120(d).

%F a(n) = A083254(n) - A297114(n).

%F a(2n) = 0.

%o (PARI) A297115(n) = sumdiv(n,d,moebius(n/d)*hammingweight(d));

%Y Cf. A000120, A008683, A083254, A297114, A297116 (odd bisection), A297117.

%K sign

%O 1,7

%A _Antti Karttunen_, Dec 26 2017

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Last modified April 24 00:30 EDT 2024. Contains 371917 sequences. (Running on oeis4.)