A354987 a(n) = A344005(n) / gcd(A047994(n), A344005(n)).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jun 16 2022

Keywords

• nonn
• frac

Comments

Denominator of fraction A047994(n) / A344005(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A047994, A344005, A346607, A354985, A354986 (numerators).

Cf. also A345998, A345999.

Programs

Mathematica

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 *)

PARI

A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
A354987(n) = { my(u=A344005(n)); (u/gcd(u, A047994(n))); };

Formula

a(n) = A344005(n) / A354985(n) = A344005(n) / gcd(A047994(n), A344005(n)).