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Difference between A294898 and its Möbius transform (A297114).
4

%I #7 Aug 10 2018 09:07:03

%S 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 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 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 Difference between A294898 and its Möbius transform (A297114).

%H Antti Karttunen, <a href="/A317844/b317844.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = -Sum_{d|n, d<n} A008683(n/d)*A294898(d).

%F a(n) = A294898(n) - A297114(n).

%F a(n) = A300244(n) - A001065(n).

%o (PARI)

%o A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };

%o A317844(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*(A005187(d)-sigma(d)));

%Y Cf. A000203, A001065, A005187, A008683, A294898, A297114, A300244.

%K sign

%O 1,10

%A _Antti Karttunen_, Aug 09 2018