A319677 Denominator of A047994(n)/n where A047994 is the unitary totient function.

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 2, 13, 7, 15, 16, 17, 9, 19, 5, 7, 11, 23, 12, 25, 13, 27, 14, 29, 15, 31, 32, 33, 17, 35, 3, 37, 19, 13, 10, 41, 7, 43, 22, 45, 23, 47, 8, 49, 25, 51, 13, 53, 27, 11, 4, 19, 29, 59, 5, 61, 31, 21, 64, 65, 33, 67, 17, 69, 35, 71

Offset: 1

Author

Michel Marcus, Sep 26 2018

Keywords

• nonn
• frac

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A047994, A030163, A305678, A319481, A319676 (numerators), A323409, A331177 (ordinal transform).

Cf. A002110, A060753.

Programs

Mathematica

uphi[n_] := Product[{p, e} = pe; p^e - 1, {pe, FactorInteger[n]}];
a[n_] := Denominator[uphi[n]/n];
Array[a, 100] (* Jean-François Alcover, Jan 10 2022 *)

PARI

a(n)=my(f=factor(n)~); denominator(prod(i=1, #f, f[1, i]^f[2, i]-1)/n);

Formula

a(p) = p, for p prime.

a(A002110(n)) = A060753(n).

a(n) = n / A323409(n) = n / gcd(n, A047994(n)). - Antti Karttunen, Jan 11 2020