A300720 - OEIS

%I #9 Mar 14 2018 03:49:23

%S 0,0,0,1,0,3,0,2,2,5,0,6,0,7,6,4,0,9,0,10,8,11,0,12,4,13,6,14,0,21,0,

%T 8,12,17,10,20,0,19,14,20,0,29,0,22,18,23,0,24,6,25,18,26,0,27,14,28,

%U 20,29,0,42,0,31,24,16,16,45,0,34,24,45,0,40,0,37,30,38,16,53,0,40,18,41,0,58,20,43,30,44,0,63,18

%N Difference between A010848 and its Möbius transform.

%H Antti Karttunen, <a href="/A300720/b300720.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = -Sum_{d|n, d<n} A008683(n/d)*A010848(d).

%F a(n) = A010848(n) - A300718(n).

%o (PARI)

%o A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0,f[i, 2]-1)); factorback(f); }; \\ From A003557

%o A010848(n) = (n - A003557(n));

%o A300720(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A010848(d));

%Y Cf. A008683, A003557, A010848, A300718.

%K nonn

%O 1,6

%A _Antti Karttunen_, Mar 12 2018