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A297171 Möbius transform of A243071.

%I A297171 #10 Dec 28 2017 19:35:05
%S A297171 0,1,3,1,7,2,15,2,2,6,31,5,63,14,3,4,127,2,255,13,11,30,511,10,4,62,4,
%T A297171 29,1023,4,2047,8,27,126,5,4,4095,254,59,26,8191,12,16383,61,10,510,
%U A297171 32767,20,8,4,123,125,65535,4,21,58,251,1022,131071,7,262143,2046,26,16,53,28,524287,253,507,6,1048575,8
%N A297171 Möbius transform of A243071.
%H A297171 Antti Karttunen, <a href="/A297171/b297171.txt">Table of n, a(n) for n = 1..4096</a>
%F A297171 a(n) = Sum_{d|n} A008683(n/d)*A243071(d).
%o A297171 (PARI)
%o A297171 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 A297171 A243071(n) = if(n<=2, n-1, if(!(n%2), 2*A243071(n/2), 1+(2*A243071(A064989(n)))));
%o A297171 A297171(n) = sumdiv(n,d,moebius(n/d)*A243071(d));
%Y A297171 Cf. A008683, A064989, A243071, A297161 (rgs-transform of this sequence).
%Y A297171 Cf. also A297112, A297156, A297172.
%K A297171 nonn
%O A297171 1,3
%A A297171 _Antti Karttunen_, Dec 26 2017