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A322994 Möbius transform of A322993.

%I A322994 #10 Jan 05 2019 13:21:05
%S A322994 0,1,1,2,1,3,1,4,2,7,1,4,1,15,3,8,1,6,1,8,7,31,1,8,2,63,4,16,1,5,1,16,
%T A322994 15,127,3,8,1,255,31,16,1,9,1,32,4,511,1,16,2,14,63,64,1,12,7,32,127,
%U A322994 1023,1,8,1,2047,8,32,15,17,1,128,255,13,1,16,1,4095,6,256,3,33,1,32,8,8191,1,16,31,16383,511,64,1,12,7,512,1023
%N A322994 Möbius transform of A322993.
%C A322994 Möbius transform of A000265(A156552(n)).
%H A322994 Antti Karttunen, <a href="/A322994/b322994.txt">Table of n, a(n) for n = 1..8192</a>
%F A322994 a(n) = Sum_{d|n} A008683(n/d)*A322993(d).
%o A322994 (PARI)
%o A322994 A000265(n) = (n/2^valuation(n, 2));
%o A322994 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A322994 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
%o A322994 A322993(n) = if(1==n,0,A000265(A156552(n)));
%o A322994 A322994(n) = sumdiv(n,d,moebius(n/d)*A322993(d));
%Y A322994 Cf. A000265, A008683, A156552, A297112, A322993.
%K A322994 nonn
%O A322994 1,4
%A A322994 _Antti Karttunen_, Jan 02 2019