%I #11 Jul 06 2021 20:06:04
%S 1,1,1,1,1,1,1,1,1,2,1,3,1,3,2,1,1,7,1,1,3,5,1,5,1,6,1,1,1,4,1,1,5,8,
%T 3,21,1,9,6,5,1,3,1,1,7,11,1,11,1,21,8,1,1,1,5,15,9,14,1,3,1,15,21,1,
%U 6,5,1,1,11,4,1,5,1,18,21,1,5,3,1,11,1,20,1,2,8,21,14,5,1,7,6,1,15,23,9,21,1,43,1,1,1,4
%N a(n) = A206369(n) / gcd(A071324(n), A206369(n)).
%H Antti Karttunen, <a href="/A345063/b345063.txt">Table of n, a(n) for n = 1..14161</a>
%H Antti Karttunen, <a href="/A345063/a345063.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F a(n) = A206369(n) / A345061(n) = A206369(n) / gcd(A071324(n), A206369(n)).
%t {1}~Join~Array[#2/GCD @@ {##} & @@ {Total[-#*(-1)^Range[Length[#], 1, -1]] &@ Divisors[#], Times @@ (Sum[(-1)^(#2 - k)*#1^k, {k, 0, #2}] & @@@ FactorInteger[#])} &, 101, 2] (* _Michael De Vlieger_, Jul 06 2021, after _Amiram Eldar_ at A071324 and A206369 *)
%o (PARI)
%o A071324(n) = my(d=Vecrev(divisors(n))); sum(k=1, #d, (-1)^(k+1)*d[k]); \\ From A071324
%o A206369(n) = sumdiv(n, d, eulerphi(n/d) * issquare(d)); \\ From A206369
%o A345063(n) = { my(u=A206369(n)); (u/gcd(u, A071324(n))); };
%Y Cf. A071324, A206369, A345060, A345061, A345062, A345064.
%K nonn
%O 1,10
%A _Antti Karttunen_, Jun 07 2021