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A297156 Möbius transform of A243354.

%I A297156 #5 Dec 28 2017 19:33:53
%S A297156 0,1,3,1,7,2,15,3,1,6,31,6,63,14,2,5,127,2,255,14,10,30,511,10,1,62,7,
%T A297156 30,1023,4,2047,11,26,126,2,2,4095,254,58,26,8191,12,16383,62,14,510,
%U A297156 32767,22,1,2,122,126,65535,6,18,58,250,1022,131071,4,262143,2046,30,21,50,28,524287,254,506,4,1048575,6
%N A297156 Möbius transform of A243354.
%H A297156 Antti Karttunen, <a href="/A297156/b297156.txt">Table of n, a(n) for n = 1..4096</a>
%o A297156 (PARI)
%o A297156 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 A297156 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
%o A297156 A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ Essentially _Joerg Arndt_'s Jul 19 2012 code.
%o A297156 A243354(n) = A006068(A156552(n));
%o A297156 A297156(n) = sumdiv(n,d,moebius(n/d)*A243354(d));
%Y A297156 Cf. A006068, A156552, A243354, A297157 (rgs-transform of this sequence).
%Y A297156 Cf. also A297112, A297171, A297172.
%K A297156 nonn
%O A297156 1,3
%A A297156 _Antti Karttunen_, Dec 28 2017