cp's OEIS Frontend

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

%I A014973 #70 Dec 30 2024 21:53:17
%S A014973 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,
%T A014973 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,
%U A014973 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
%N A014973 a(n) = n / gcd(n, (n-1)!).
%C A014973 Denominator in n!/n^2. Also denominator in Taylor series expansion of dilog function (also called Li_2). - _Ralf Stephan_, Mar 28 2004
%H A014973 Vincenzo Librandi, <a href="/A014973/b014973.txt">Table of n, a(n) for n = 1..10000</a>
%F A014973 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
%F A014973 a(n) = denominator((n-1)! * Sum_{i=1..n} (1 - 1/i)). - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 16 2004
%F A014973 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
%F A014973 a(n) = denominator((-1)^n*n!/(1+n)). - _Stefano Spezia_, Jun 24 2024
%p A014973 seq(n / igcd(n, (n-1)!), n = 1..88);  # _Peter Luschny_, Nov 02 2022
%t A014973 Table[n/GCD[n,(n-1)!],{n,90}] (* _Harvey P. Dale_, Mar 16 2012 *)
%t A014973 Table[Denominator[n!/n^2], {n, 1, 100}] (* _Vincenzo Librandi_, Apr 15 2014 *)
%o A014973 (Magma) [Denominator(Factorial(n)/n^2): n in [1..80]]; // _Vincenzo Librandi_, Apr 15 2014
%o A014973 (PARI) a(n)=numerator(polcoeff((x+1)*exp(x+x*O(x^(n-1))), n-1)); \\ _Gerry Martens_, Aug 12 2015
%o A014973 (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 }
%o A014973 val(n, p) = my(r=0); while(n, r+=n\=p); r \\ _David A. Corneth_, Oct 27 2022
%o A014973 (PARI) a(n) = if(n == 4, return(2), return(n^isprime(n))) \\ _David A. Corneth_, Oct 27 2022
%Y A014973 Cf. A092043.
%K A014973 nonn,easy
%O A014973 1,2
%A A014973 _Marc LeBrun_