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%I #14 Jun 16 2022 21:19:00
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,1,1,1,1,1,4,1,1,1,7,1,5,1,1,11,1,
%T 7,1,1,1,1,15,1,1,1,11,9,1,1,1,1,1,17,1,1,1,1,1,1,1,1,5,1,1,9,1,25,11,
%U 1,1,23,7,1,1,1,1,1,19,7,1,1,1,1,1,1,5,17,1,29,16,1,9,13,23,1,1,19,16,1,1,11,1,1,17
%N a(n) = A344005(n) / gcd(A047994(n), A344005(n)).
%C Denominator of fraction A047994(n) / A344005(n).
%H Antti Karttunen, <a href="/A354987/b354987.txt">Table of n, a(n) for n = 1..20000</a>
%H Antti Karttunen, <a href="/A354987/a354987.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F a(n) = A344005(n) / A354985(n) = A344005(n) / gcd(A047994(n), A344005(n)).
%t s[n_] := Module[{m = 1}, While[!Divisible[m*(m + 1), n], m++]; m]; f[p_, e_] := p^e - 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; uphi[1] = 1; a[n_] := Denominator[uphi[n]/s[n]]; Array[a, 100] (* _Amiram Eldar_, Jun 16 2022 *)
%o (PARI)
%o A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
%o A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
%o A354987(n) = { my(u=A344005(n)); (u/gcd(u, A047994(n))); };
%Y Cf. A047994, A344005, A346607, A354985, A354986 (numerators).
%Y Cf. also A345998, A345999.
%K nonn,frac
%O 1,15
%A _Antti Karttunen_, Jun 16 2022
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