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

1,4

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

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

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 *)

Prog

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

Crossrefs

Sequence in context: A354433 A378664 A005451 * A113520 A232597 A197008

Adjacent sequences: A135680 A135681 A135682 * A135684 A135685 A135686

Keyword

dead

Author

Mohammad K. Azarian, Dec 01 2007

Status

approved