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A300822 Möbius transform of A300222.

%I A300822 #12 Mar 19 2018 22:14:06
%S A300822 0,2,0,-2,2,4,6,8,0,-4,2,-4,0,-6,4,-2,8,12,18,22,12,14,20,16,22,24,0,
%T A300822 0,2,-8,0,-4,4,-4,0,-12,0,-18,0,-28,2,-12,6,-8,12,-4,20,-4,12,-2,16,0,
%U A300822 26,36,50,48,36,50,56,44,60,60,36,52,54,28,54,52,40,60,62,48,72,72,44,72,66,48,78,82,0,-4,2,0,-10,-6,4,-10,8,-24,-6,-14,0
%N A300822 Möbius transform of A300222.
%H A300822 Antti Karttunen, <a href="/A300822/b300822.txt">Table of n, a(n) for n = 1..65537</a>
%F A300822 a(n) = Sum_{d|n} moebius(n/d)*A300222(d).
%F A300822 a(n) = A000010(n) - A300821(n).
%F A300822 a(n) = A300222(n) - A300824(n).
%t A300822 Table[DivisorSum[n, MoebiusMu[n/#] FromDigits[IntegerDigits[#, 3] /. 1 -> 0, 3] &], {n, 93}] (* _Michael De Vlieger_, Mar 17 2018 *)
%o A300822 (PARI)
%o A300822 A300222(n) = fromdigits(apply(x->(if (1==x, 0, x)), digits(n, 3)), 3);
%o A300822 A300822(n) = sumdiv(n,d,moebius(n/d)*A300222(d));
%Y A300822 Cf. A000010, A300222, A300821, A300824.
%K A300822 sign,base
%O A300822 1,2
%A A300822 _Antti Karttunen_, Mar 14 2018