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A135683 a(n)=1 if n is a prime number; otherwise, a(n)=n. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

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-Fran├žois 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

Cf. A000027, A000040, A135679, A135680, A014681, A014682, A014683, A014684, A014685, A014686, A014687, A014688, A014689, A014690, A135681, A135682.

Sequence in context: A324118 A100796 A005451 * A113520 A232597 A197008

Adjacent sequences:  A135680 A135681 A135682 * A135684 A135685 A135686

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian, Dec 01 2007

STATUS

approved

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Last modified August 3 14:40 EDT 2021. Contains 346438 sequences. (Running on oeis4.)