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A300720 Difference between A010848 and its Möbius transform.

%I A300720 #9 Mar 14 2018 03:49:23
%S A300720 0,0,0,1,0,3,0,2,2,5,0,6,0,7,6,4,0,9,0,10,8,11,0,12,4,13,6,14,0,21,0,
%T A300720 8,12,17,10,20,0,19,14,20,0,29,0,22,18,23,0,24,6,25,18,26,0,27,14,28,
%U A300720 20,29,0,42,0,31,24,16,16,45,0,34,24,45,0,40,0,37,30,38,16,53,0,40,18,41,0,58,20,43,30,44,0,63,18
%N A300720 Difference between A010848 and its Möbius transform.
%H A300720 Antti Karttunen, <a href="/A300720/b300720.txt">Table of n, a(n) for n = 1..65537</a>
%F A300720 a(n) = -Sum_{d|n, d<n} A008683(n/d)*A010848(d).
%F A300720 a(n) = A010848(n) - A300718(n).
%o A300720 (PARI)
%o A300720 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0,f[i, 2]-1)); factorback(f); }; \\ From A003557
%o A300720 A010848(n) = (n - A003557(n));
%o A300720 A300720(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A010848(d));
%Y A300720 Cf. A008683, A003557, A010848, A300718.
%K A300720 nonn
%O A300720 1,6
%A A300720 _Antti Karttunen_, Mar 12 2018