A135683 Duplicate of A005451.

1, 1, 1, 4, 1, 6, 1, 8, 9, 10, 1, 12, 1, 14, 15, 16, 1, 18, 1, 20, 21, 22, 1, 24, 25, 26, 27, 28, 1, 30, 1, 32, 33, 34, 35, 36, 1, 38, 39, 40, 1, 42, 1, 44, 45, 46, 1, 48, 49, 50, 51, 52, 1, 54, 55, 56, 57, 58, 1, 60, 1, 62, 63

Offset: 1

Author

Mohammad K. Azarian, Dec 01 2007

Keywords

• dead

Comments

Previous name was: a(n) = 1 if n is a prime number, otherwise, a(n) = n.

References

• Paulo Ribenboim, The little book of big primes, Springer 1991, p. 106.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[IsPrime(n) select 1 else n: n in [1..70]]; // Vincenzo Librandi, Feb 22 2013

Maple

seq(denom((1 + (n-1)!)/n), n=1..80); # G. C. Greubel, Nov 22 2022

Mathematica

Table[If[PrimeQ[n], 1, n], {n, 70}] (* Vincenzo Librandi, Feb 22 2013 *)
a[n_] := ((n-1)! + 1)/n - Floor[(n-1)!/n] // Denominator; Table[a[n] , {n, 1, 63}] (* Jean-François Alcover, Jul 17 2013, after Minac's formula *)

Sage

def A135683(n):
    if n == 4: return n
    f = factorial(n-1)
    return 1/((f + 1)/n - f//n)
[A135683(n) for n in (1..63)]   # Peter Luschny, Oct 16 2013

Formula

a(n) = A088140(n), n >= 3. - R. J. Mathar, Oct 28 2008

a(n) = gcd(n, (n!*n!!)/n^2). - Lechoslaw Ratajczak, Mar 09 2019

a(n) = A005451(n), for n >= 2. - G. C. Greubel, Nov 22 2022