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A297172 Möbius transform of A253564.

%I A297172 #8 Dec 28 2017 19:35:13
%S A297172 0,1,3,1,7,1,15,2,3,3,31,3,63,7,3,4,127,2,255,7,9,15,511,6,7,31,6,15,
%T A297172 1023,3,2047,8,21,63,7,4,4095,127,45,14,8191,7,16383,31,9,255,32767,
%U A297172 12,15,4,93,63,65535,4,21,30,189,511,131071,5,262143,1023,21,16,49,15,524287,127,381,5,1048575,8,2097151,2047,6
%N A297172 Möbius transform of A253564.
%H A297172 Antti Karttunen, <a href="/A297172/b297172.txt">Table of n, a(n) for n = 1..4096</a>
%F A297172 a(n) = Sum_{d|n} A008683(n/d)*A253564(d).
%o A297172 (PARI)
%o A297172 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 A297172 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A297172 A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
%o A297172 A253564(n) = A156552(A122111(n));
%o A297172 A297172(n) = sumdiv(n,d,moebius(n/d)*A253564(d));
%Y A297172 Cf. A008683, A064989, A122111, A156552, A253564, A297162 (rgs-transform of this sequence).
%Y A297172 Cf. also A297112, A297156, A297171.
%K A297172 nonn
%O A297172 1,3
%A A297172 _Antti Karttunen_, Dec 26 2017