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A300236 Möbius transform of A032742 (the largest proper divisor of n).

%I A300236 #13 Mar 14 2018 03:50:24
%S A300236 1,0,0,1,0,2,0,2,2,4,0,2,0,6,4,4,0,4,0,4,6,10,0,4,4,12,6,6,0,4,0,8,10,
%T A300236 16,6,6,0,18,12,8,0,6,0,10,8,22,0,8,6,16,16,12,0,12,10,12,18,28,0,8,0,
%U A300236 30,12,16,12,10,0,16,22,18,0,12,0,36,16,18,10,12,0,16,18,40,0,12,16,42,28,20,0,16,12,22,30,46,18,16,0,36
%N A300236 Möbius transform of A032742 (the largest proper divisor of n).
%H A300236 Antti Karttunen, <a href="/A300236/b300236.txt">Table of n, a(n) for n = 1..65537</a>
%F A300236 a(n) = Sum_{d|n} A008683(n/d)*A032742(d).
%t A300236 Table[DivisorSum[n, # MoebiusMu[n/#]/FactorInteger[#][[1, 1]] &], {n, 98}] (* _Michael De Vlieger_, Mar 10 2018 *)
%o A300236 (PARI)
%o A300236 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A300236 A300236(n) = sumdiv(n,d,moebius(n/d)*A032742(d));
%Y A300236 Cf. A008683, A032742, A300239.
%K A300236 nonn
%O A300236 1,6
%A A300236 _Antti Karttunen_, Mar 10 2018