A352482 Denominator of (n-d)/n*d where d = A000005(n) is the number of divisors of n.

1, 1, 6, 12, 10, 12, 14, 8, 9, 20, 22, 12, 26, 28, 60, 80, 34, 9, 38, 60, 84, 44, 46, 12, 75, 52, 108, 84, 58, 120, 62, 96, 132, 68, 140, 12, 74, 76, 156, 10, 82, 168, 86, 132, 90, 92, 94, 240, 147, 75, 204, 156, 106, 216, 220, 28, 228, 116, 118, 15, 122, 124, 126, 448, 260, 264, 134

Offset: 1

Author

Michel Marcus, Mar 18 2022

Keywords

• nonn
• frac

Comments

The terms are of course the denominators of the fraction "in smallest terms", otherwise said: a(n) = n*d/gcd(n*d, n - d), which is unambiguous also for n = 1 and n = 2 where n - d = 0.

Examples

			The number n = 1 has d = 1 divisors, so (n-d)/(n*d) = 0/1 has denominator a(1) = 1.
The number n = 2 has d = 2 divisors, so (n-d)/(n*d) = 0/4 = 0/1 has denominator a(2) =  1 when written in smallest terms.
The number n = 3 has d = 2 divisors, so (n-d)/(n*d) = 1/6 has denominator a(3) =  6.
The number n = 4 has d = 3 divisors, so (n-d)/(n*d) = 1/12 has denominator a(4) = 12.
The number n = 6 has d = 4 divisors, so (n-d)/(n*d) = 2/24 = 1/12 has denominator a(6) = 12.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..10000 (terms a(3..10^4) from Michel Marcus), Apr 17 2022

Crossrefs

Cf. A000005, A049820, A146566, A352483 (numerator).

Programs

Mathematica

a[n_] := Numerator[n*(d = DivisorSigma[0, n])/(n - d)]; Array[a, 100, 3] (* Amiram Eldar, Mar 18 2022 *)

PARI

A352482(n,d=numdiv(n))=denominator((n-d)/(n*d))

Extensions

Edited and extended to offset 1 by M. F. Hasler, Apr 17 2022