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A345939 a(n) = (n-1) / gcd(n-1, uphi(n)), where uphi is unitary totient (or unitary phi) function, A047994.

%I A345939 #14 Jul 04 2021 06:16:45
%S A345939 0,1,1,1,1,5,1,1,1,9,1,11,1,13,7,1,1,17,1,19,5,21,1,23,1,25,1,3,1,29,
%T A345939 1,1,8,33,17,35,1,37,19,39,1,41,1,43,11,45,1,47,1,49,25,17,1,53,27,55,
%U A345939 14,57,1,59,1,61,31,1,4,13,1,67,17,23,1,71,1,73,37,25,19,77,1,79,1,81,1,83,21,85,43,87,1,89,5,91
%N A345939 a(n) = (n-1) / gcd(n-1, uphi(n)), where uphi is unitary totient (or unitary phi) function, A047994.
%H A345939 Antti Karttunen, <a href="/A345939/b345939.txt">Table of n, a(n) for n = 1..16384</a>
%H A345939 Antti Karttunen, <a href="/A345939/a345939.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A345939 a(n) = (n-1) / A345937(n) = (n-1) / gcd(n-1, A047994(n)).
%F A345939 a(2n-1) = A345949(2n-1), for n > 1.
%t A345939 uphi[1]=1;uphi[n_]:=Times@@(#[[1]]^#[[2]]-1&/@FactorInteger[n]);
%t A345939 a[n_]:=(n-1)/GCD[n-1,uphi[n]];Array[a,100] (* _Giorgos Kalogeropoulos_, Jul 02 2021 *)
%o A345939 (PARI)
%o A345939 A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
%o A345939 A345939(n) = ((n-1) / gcd(n-1, A047994(n)));
%Y A345939 Cf. A047994, A345937, A345938.
%Y A345939 Cf. also A160596, A340089, A345949.
%K A345939 nonn
%O A345939 1,6
%A A345939 _Antti Karttunen_, Jun 29 2021