cp's OEIS Frontend

A317844 Difference between A294898 and its Möbius transform (A297114).

%I A317844 #7 Aug 10 2018 09:07:03
%S A317844 0,0,0,0,0,0,0,0,0,2,0,-2,0,3,2,0,0,1,0,0,3,7,0,-6,2,9,3,1,0,-2,0,0,7,
%T A317844 14,5,-9,0,15,9,-4,0,3,0,5,5,18,0,-14,3,14,14,7,0,2,9,-3,15,24,0,-24,
%U A317844 0,25,10,0,11,12,0,12,18,15,0,-29,0,33,16,13,10,14,0,-12,10,37,0,-23,16,38,24,1,0,-16,12,16,25
%N A317844 Difference between A294898 and its Möbius transform (A297114).
%H A317844 Antti Karttunen, <a href="/A317844/b317844.txt">Table of n, a(n) for n = 1..65537</a>
%F A317844 a(n) = -Sum_{d|n, d<n} A008683(n/d)*A294898(d).
%F A317844 a(n) = A294898(n) - A297114(n).
%F A317844 a(n) = A300244(n) - A001065(n).
%o A317844 (PARI)
%o A317844 A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
%o A317844 A317844(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*(A005187(d)-sigma(d)));
%Y A317844 Cf. A000203, A001065, A005187, A008683, A294898, A297114, A300244.
%K A317844 sign
%O A317844 1,10
%A A317844 _Antti Karttunen_, Aug 09 2018