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A300722 Difference between A060681 (largest difference between consecutive divisors of n as ordered by size) and its Möbius transform.

%I A300722 #9 Mar 14 2018 03:49:32
%S A300722 0,0,0,1,0,3,0,2,2,5,0,4,0,7,6,4,0,7,0,6,8,11,0,8,4,13,6,8,0,11,0,8,
%T A300722 12,17,10,12,0,19,14,12,0,15,0,12,14,23,0,16,6,21,18,14,0,21,14,16,20,
%U A300722 29,0,22,0,31,18,16,16,23,0,18,24,29,0,24,0,37,26,20,16,27,0,24,18,41,0,30,20,43,30,24,0,37,18,24,32,47,22,32
%N A300722 Difference between A060681 (largest difference between consecutive divisors of n as ordered by size) and its Möbius transform.
%H A300722 Antti Karttunen, <a href="/A300722/b300722.txt">Table of n, a(n) for n = 1..65537</a>
%F A300722 a(n) = -Sum_{d|n, d<n} A008683(n/d)*A060681(d).
%F A300722 a(n) = A060681(n) - A300721(n).
%o A300722 (PARI)
%o A300722 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A300722 A060681(n) = (n-A032742(n));
%o A300722 A300722(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A060681(d));
%K A300722 nonn
%O A300722 1,6
%A A300722 _Antti Karttunen_, Mar 11 2018