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A364558 a(n) = A364557(n) - A000010(n), where A364557 is the Möbius transform of A005941, and A000010 (Euler phi) is the Möbius transform of A000027.

%I A364558 #17 Jul 29 2023 15:58:46
%S A364558 0,0,0,0,0,0,2,0,-2,0,6,0,20,2,-4,0,48,-2,110,0,-4,6,234,0,-12,20,-10,
%T A364558 4,484,-4,994,0,-4,48,-16,-4,2012,110,8,0,4056,-4,8150,12,-16,234,
%U A364558 16338,0,-26,-12,32,40,32716,-10,-24,8,92,484,65478,-8,131012,994,-20,0,-16,-4,262078,96,212,-16,524218,-8,1048504
%N A364558 a(n) = A364557(n) - A000010(n), where A364557 is the Möbius transform of A005941, and A000010 (Euler phi) is the Möbius transform of A000027.
%H A364558 Antti Karttunen, <a href="/A364558/b364558.txt">Table of n, a(n) for n = 1..10000</a>
%o A364558 (PARI) A364558(n) = (A364557(n)-eulerphi(n));
%o A364558 (Python)
%o A364558 from math import prod
%o A364558 from sympy import factorint, primepi
%o A364558 def A364558(n): return (1<<primepi(max(f:=factorint(n)))+sum(e-1 for e in f.values())-1)-prod(p**(e-1)*(p-1) for p, e in f.items()) if n>1 else 0 # _Chai Wah Wu_, Jul 29 2023
%Y A364558 Cf. A000010, A005941, A364557, A364559 (inverse Möbius transform), A364565 (positions of 0's), A364566 (of terms < 0).
%K A364558 sign
%O A364558 1,7
%A A364558 _Antti Karttunen_, Jul 28 2023