A014973 a(n) = n / gcd(n, (n-1)!).

1, 2, 3, 2, 5, 1, 7, 1, 1, 1, 11, 1, 13, 1, 1, 1, 17, 1, 19, 1, 1, 1, 23, 1, 1, 1, 1, 1, 29, 1, 31, 1, 1, 1, 1, 1, 37, 1, 1, 1, 41, 1, 43, 1, 1, 1, 47, 1, 1, 1, 1, 1, 53, 1, 1, 1, 1, 1, 59, 1, 61, 1, 1, 1, 1, 1, 67, 1, 1, 1, 71, 1, 73, 1, 1, 1, 1, 1, 79, 1, 1, 1, 83, 1, 1, 1, 1

Offset: 1

Author

Marc LeBrun

Keywords

• nonn
• easy

Comments

Denominator in n!/n^2. Also denominator in Taylor series expansion of dilog function (also called Li_2). - Ralf Stephan, Mar 28 2004

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A092043.

Programs

Magma

[Denominator(Factorial(n)/n^2): n in [1..80]]; // Vincenzo Librandi, Apr 15 2014

Maple

seq(n / igcd(n, (n-1)!), n = 1..88);  # Peter Luschny, Nov 02 2022

Mathematica

Table[n/GCD[n,(n-1)!],{n,90}] (* Harvey P. Dale, Mar 16 2012 *)
Table[Denominator[n!/n^2], {n, 1, 100}] (* Vincenzo Librandi, Apr 15 2014 *)

PARI

a(n)=numerator(polcoeff((x+1)*exp(x+x*O(x^(n-1))), n-1)); \\ Gerry Martens, Aug 12 2015

PARI

a(n) = { my(f = factor(n), res = n); for(i = 1, #f~, res /= f[i, 1]^(min(f[i, 2], val(n-1, f[i, 1]))) ); res }
val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Oct 27 2022

PARI

a(n) = if(n == 4, return(2), return(n^isprime(n))) \\ David A. Corneth, Oct 27 2022

Formula

a(4) = 2; otherwise a(n) = 1 unless n is a prime in which case a(n) = n. - Ola Veshta (olaveshta(AT)my-deja.com), May 30 2001

a(n) = denominator((n-1)! * Sum_{i=1..n} (1 - 1/i)). - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 16 2004

a(n+1) equals the numerator of the coefficient of x^n in the expansion of (1 + x)*exp(x), with denominator A092043(n+1), for n >= 0. - Wolfdieter Lang, Oct 26 2022

a(n) = denominator((-1)^n*n!/(1+n)). - Stefano Spezia, Jun 24 2024