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A300824 Difference between A300222(n) and its Möbius transform.

%I A300824 #10 Mar 24 2018 18:55:16
%S A300824 0,0,0,2,0,2,0,0,0,4,0,4,0,8,2,8,0,6,0,-2,6,4,0,8,2,2,0,0,0,8,0,6,2,
%T A300824 10,8,12,0,20,0,28,0,18,0,16,6,22,0,22,6,22,8,24,0,18,4,8,18,4,0,16,0,
%U A300824 2,18,2,2,26,0,4,20,0,0,24,0,2,28,0,8,30,0,-2,0,4,0,0,10,8,2,16,0,24,6,16,0,22,20,14,0,14,6,40,0,26,0,32,24
%N A300824 Difference between A300222(n) and its Möbius transform.
%H A300824 Antti Karttunen, <a href="/A300824/b300824.txt">Table of n, a(n) for n = 1..65537</a>
%F A300824 a(n) = A300222(n) - A300822(n).
%F A300824 a(n) = -Sum_{d|n, d<n} A008683(n/d)*A300222(d) = Sum_{d|n, d<n} A300822(d).
%F A300824 a(n) = A051953(n) - A300823(n).
%t A300824 f[n_] := FromDigits[IntegerDigits[n, 3] /. 1 -> 0, 3]; Table[f@ n - DivisorSum[n, MoebiusMu[n/#] f@ # &], {n, 105}] (* _Michael De Vlieger_, Mar 17 2018 *)
%o A300824 (PARI)
%o A300824 A300222(n) = fromdigits(apply(x->(if (1==x, 0, x)), digits(n, 3)), 3);
%o A300824 A300824(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A300222(d));
%Y A300824 Cf. A008683, A051953, A300222, A300822, A300823, A300825.
%K A300824 sign,base
%O A300824 1,4
%A A300824 _Antti Karttunen_, Mar 14 2018