cp's OEIS Frontend

A353364 Inverse Möbius transform of A332814.

%I A353364 #9 Apr 16 2022 09:40:59
%S A353364 0,1,-1,1,1,-1,-1,2,-1,2,1,-2,-1,-1,1,2,1,0,-1,3,-2,2,1,-2,1,-1,-2,-2,
%T A353364 -1,1,1,3,1,2,-1,-1,-1,-1,-2,4,1,-2,-1,3,2,2,1,-3,-1,3,1,-2,-1,-2,2,
%U A353364 -2,-2,-1,1,2,-1,2,-3,3,-1,1,1,3,1,-2,-1,0,1,-1,0,-2,1,-2,-1,5,-2,2,1,-4,2,-1,-2,4,-1,3,-2,3
%N A353364 Inverse Möbius transform of A332814.
%H A353364 Antti Karttunen, <a href="/A353364/b353364.txt">Table of n, a(n) for n = 1..65537</a>
%H A353364 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353364 a(n) = Sum_{d|n} A332814(d).
%F A353364 For all n >= 1, a(A003961(n)) = -a(n), a(A000040(n)) = ((-1)^(n-1)).
%o A353364 (PARI)
%o A353364 A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A353364 A332814(n) = { my(u=A156552(n)%3); if(2==u,-1,u); };
%o A353364 A353364(n) = sumdiv(n,d,A332814(d));
%Y A353364 Cf. A003961, A156552, A332814.
%Y A353364 Cf. also A353354, A353361, A353362.
%K A353364 sign
%O A353364 1,8
%A A353364 _Antti Karttunen_, Apr 15 2022