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A300719 Difference between A003557 (n divided by largest squarefree divisor of n) and its Möbius transform.

%I A300719 #11 Mar 14 2018 03:49:18
%S A300719 0,1,1,1,1,1,1,2,1,1,1,2,1,1,1,4,1,3,1,2,1,1,1,4,1,1,3,2,1,1,1,8,1,1,
%T A300719 1,4,1,1,1,4,1,1,1,2,3,1,1,8,1,5,1,2,1,9,1,4,1,1,1,2,1,1,3,16,1,1,1,2,
%U A300719 1,1,1,8,1,1,5,2,1,1,1,8,9,1,1,2,1,1,1,4,1,3,1,2,1,1,1,16,1,7,3,6,1,1,1,4,1
%N A300719 Difference between A003557 (n divided by largest squarefree divisor of n) and its Möbius transform.
%H A300719 Antti Karttunen, <a href="/A300719/b300719.txt">Table of n, a(n) for n = 1..65537</a>
%F A300719 a(n) = -Sum_{d|n, d<n} A008683(n/d)*A003557(d).
%F A300719 a(n) = A003557(n) - A300717(n).
%o A300719 (PARI)
%o A300719 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0,f[i, 2]-1)); factorback(f); }; \\ From A003557
%o A300719 A300719(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A003557(d));
%Y A300719 Cf. A003557, A008683, A300717.
%K A300719 nonn
%O A300719 1,8
%A A300719 _Antti Karttunen_, Mar 12 2018