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A300721 Möbius transform of A060681, the largest difference between consecutive divisors of n (ordered by size).

%I A300721 #17 Jan 07 2022 03:23:07
%S A300721 0,1,2,1,4,0,6,2,4,0,10,2,12,0,4,4,16,2,18,4,6,0,22,4,16,0,12,6,28,4,
%T A300721 30,8,10,0,18,6,36,0,12,8,40,6,42,10,16,0,46,8,36,4,16,12,52,6,30,12,
%U A300721 18,0,58,8,60,0,24,16,36,10,66,16,22,6,70,12,72,0,24,18,50,12,78,16,36,0,82,12,48,0,28,20,88,8,60,22,30,0,54,16
%N A300721 Möbius transform of A060681, the largest difference between consecutive divisors of n (ordered by size).
%H A300721 Antti Karttunen, <a href="/A300721/b300721.txt">Table of n, a(n) for n = 1..65537</a>
%F A300721 a(n) = Sum_{d|n} A008683(n/d)*A060681(d).
%F A300721 a(n) = A060681(n) - A300722(n).
%F A300721 a(n) = A000010(n) - A300236(n).
%t A300721 A060681[n_] := n - n/FactorInteger[n][[1, 1]];
%t A300721 a[n_] := Sum[MoebiusMu[n/d]*A060681[d], {d, Divisors[n]}];
%t A300721 Array[a, 100] (* _Jean-François Alcover_, Jan 07 2022 *)
%o A300721 (PARI)
%o A300721 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A300721 A060681(n) = (n-A032742(n));
%o A300721 A300721(n) = sumdiv(n,d,moebius(n/d)*A060681(d));
%Y A300721 Cf. A000010, A008683, A060681, A300236, A300722, A322873 (ordinal transform).
%K A300721 nonn
%O A300721 1,3
%A A300721 _Antti Karttunen_, Mar 11 2018