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Parity of A140773, where A140773 is the inverse Möbius transform of A038548.
4

%I #12 Nov 14 2024 23:23:48

%S 1,0,0,0,0,1,0,0,0,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,1,1,

%T 1,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0,0,

%U 1,0,0,0,0,1,0,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0

%N Parity of A140773, where A140773 is the inverse Möbius transform of A038548.

%C Also parity of the inverse Möbius transform of A369253.

%H Antti Karttunen, <a href="/A369255/b369255.txt">Table of n, a(n) for n = 1..65537</a>

%H Jon Maiga, <a href="http://sequencedb.net/s/A369255">Computer-generated formulas for A369255</a>, Sequence Machine.

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = A000035(A140773(n)).

%F From _Antti Karttunen_, Nov 14 2024: (Start)

%F Following convolution formulas have been conjectured for this sequence by Sequence Machine, with both computing the first 2^20 terms correctly:

%F a(n) = Sum_{d|n} A007875(d)*A219009(n/d).

%F a(n) = Sum_{d|n} A140773(d)*A355837(n/d).

%F (End)

%o (PARI)

%o A038548(n) = sumdiv(n,d,1-(bigomega(d)%2));

%o A369255(n) = (sumdiv(n,d,A038548(d))%2);

%Y Characteristic function of A369256.

%Y Cf. A000035, A038548, A140773, A369253.

%Y Cf. A007875, A219009, A355837.

%K nonn,changed

%O 1

%A _Antti Karttunen_, Jan 24 2024