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

1,3

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.

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A315777 A372453 A279606 * A164378 A124349 A360719

Adjacent sequences: A352479 A352480 A352481 * A352483 A352484 A352485

Keyword

nonn,frac

Author

Michel Marcus, Mar 18 2022

Extensions

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

Status

approved