cp's OEIS Frontend

A354986 a(n) = A047994(n) / gcd(A047994(n), A344005(n)).

%I A354986 #14 Jun 16 2022 21:18:56
%S A354986 1,1,1,1,1,1,1,1,1,1,1,2,1,1,8,1,1,1,1,3,2,1,1,7,1,1,1,18,1,8,1,1,20,
%T A354986 1,12,3,1,1,2,28,1,2,1,30,32,1,1,2,1,1,32,3,1,1,4,6,2,1,1,8,1,1,16,1,
%U A354986 48,20,1,3,44,12,1,7,1,1,2,54,20,2,1,4,1,1,1,9,32,1,56,35,1,32,72,66,2,1,72,31,1,1,20
%N A354986 a(n) = A047994(n) / gcd(A047994(n), A344005(n)).
%C A354986 Numerator of fraction A047994(n) / A344005(n).
%H A354986 Antti Karttunen, <a href="/A354986/b354986.txt">Table of n, a(n) for n = 1..20000</a>
%H A354986 Antti Karttunen, <a href="/A354986/a354986.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A354986 a(n) = A047994(n) / A354985(n) = A047994(n) / gcd(A047994(n), A344005(n)).
%t A354986 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_] := Numerator[uphi[n]/s[n]]; Array[a, 100] (* _Amiram Eldar_, Jun 16 2022 *)
%o A354986 (PARI)
%o A354986 A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
%o A354986 A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
%o A354986 A354986(n) = { my(u=A047994(n)); (u/gcd(u, A344005(n))); };
%Y A354986 Cf. A047994, A344005, A346607, A346608 (positions of terms > 1), A354928 (positions of 1's), A354985, A354987 (denominators).
%K A354986 nonn,frac
%O A354986 1,12
%A A354986 _Antti Karttunen_, Jun 16 2022