A175506 Denominators of the antiharmonic means B of numbers k such that gcd(k, n) = 1 for numbers n >= 1 and k < n.

1, 1, 3, 2, 1, 3, 3, 4, 9, 1, 1, 6, 3, 3, 3, 8, 1, 9, 3, 2, 3, 1, 1, 12, 5, 3, 27, 6, 1, 3, 3, 16, 3, 1, 3, 18, 3, 3, 3, 4, 1, 3, 3, 2, 9, 1, 1, 24, 21, 5, 3, 6, 1, 27, 1, 12, 3, 1, 1, 6, 3, 3, 9, 32, 3, 3, 3, 2, 3, 3, 1, 36, 3, 3, 15, 6, 3, 3, 3, 8, 81, 1, 1, 6, 1, 3, 3, 4, 1, 9, 1, 2, 3, 1, 3, 48, 3, 21, 9

Offset: 1

Author

Jaroslav Krizek, May 31 2010

Keywords

• nonn

Comments

See A175505 - numerators of the antiharmonic means B of numbers k such that gcd(k, n) = 1 for numbers n >= 1 and k < n where B = A053818(n) / A023896(n) = A175505(n) / a(n).

Programs

Mathematica

f[n_] := 2Plus @@ (Select[ Range@n, GCD[ #, n] == 1 &]^2)/(n*EulerPhi@n); f[1] = 1; Denominator@ Array[f, 80] (* Robert G. Wilson v, Jul 01 2010 *)

Formula

a(n) = A175505(n) * A023896(n) / A053818(n).

Extensions

More terms from Robert G. Wilson v, Jul 01 2010