A135683 - OEIS

%I #30 Nov 22 2022 22:18:46

%S 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,

%T 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,

%U 1,54,55,56,57,58,1,60,1,62,63

%N Duplicate of A005451.

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

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

%H Vincenzo Librandi, <a href="/A135683/b135683.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A088140(n), n >= 3. - _R. J. Mathar_, Oct 28 2008

%F a(n) = gcd(n, (n!*n!!)/n^2). - _Lechoslaw Ratajczak_, Mar 09 2019

%F a(n) = A005451(n), for n >= 2. - _G. C. Greubel_, Nov 22 2022

%p seq(denom((1 + (n-1)!)/n), n=1..80); # _G. C. Greubel_, Nov 22 2022

%t Table[If[PrimeQ[n], 1, n], {n, 70}] (* _Vincenzo Librandi_, Feb 22 2013 *)

%t 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 *)

%o (Magma) [IsPrime(n) select 1 else n: n in [1..70]]; // _Vincenzo Librandi_, Feb 22 2013

%o (Sage)

%o def A135683(n):

%o     if n == 4: return n

%o     f = factorial(n-1)

%o     return 1/((f + 1)/n - f//n)

%o [A135683(n) for n in (1..63)]   # _Peter Luschny_, Oct 16 2013

%K dead

%O 1,4

%A _Mohammad K. Azarian_, Dec 01 2007