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A300718 Möbius transform of A010848, number of numbers k <= n such that at least one prime factor of n is not a prime factor of k.

%I A300718 #13 Mar 14 2018 03:49:13
%S A300718 0,1,2,1,4,2,6,2,4,4,10,4,12,6,8,4,16,6,18,8,12,10,22,8,16,12,12,12,
%T A300718 28,8,30,8,20,16,24,10,36,18,24,16,40,12,42,20,24,22,46,16,36,20,32,
%U A300718 24,52,18,40,24,36,28,58,16,60,30,36,16,48,20,66,32,44,24,70,20,72,36,40,36,60,24,78,32,36,40,82,24,64,42,56,40,88,24,72
%N A300718 Möbius transform of A010848, number of numbers k <= n such that at least one prime factor of n is not a prime factor of k.
%H A300718 Antti Karttunen, <a href="/A300718/b300718.txt">Table of n, a(n) for n = 1..65537</a>
%F A300718 a(n) = Sum_{d|n} A008683(n/d)*A010848(d).
%F A300718 a(n) = A000010(n) - A300717(n).
%F A300718 a(n) = A010848(n) - A300720(n).
%o A300718 (PARI)
%o A300718 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0,f[i, 2]-1)); factorback(f); }; \\ From A003557
%o A300718 A010848(n) = (n - A003557(n));
%o A300718 A300718(n) = sumdiv(n,d,moebius(n/d)*A010848(d));
%Y A300718 Cf. A000010, A008683, A003557, A010848, A300717, A300720.
%K A300718 nonn
%O A300718 1,3
%A A300718 _Antti Karttunen_, Mar 11 2018