OFFSET
1,3
COMMENTS
Conjecture: a(n) = 1 if and only if n+1 is prime.
MAPLE
b:= proc(n) b(n):= (-(-1)^n/n +`if`(n=1, 0, b(n-1))) end:
g:= proc(n) g(n):= (f-> igcd(b(n)*f, f))(n!) end:
a:= n-> g(n+1)/g(n):
seq(a(n), n=1..80); # Alois P. Heinz, May 20 2020
MATHEMATICA
b[n_] := b[n] = -(-1)^n/n + If[n==1, 0, b[n-1]];
g[n_] := GCD[b[n] #, #]&[n!];
a[n_] := g[n+1]/g[n];
Array[a, 80] (* Jean-François Alcover, Nov 30 2020, after Alois P. Heinz *)
PROG
(PARI) f(n) = n!*sum(k=2, n, (-1)^k/k); \\ A024168
g(n) = gcd(f(n+1), f(n)); \\ A334958
a(n) = g(n+1)/g(n); \\ Michel Marcus, May 20 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Petros Hadjicostas, May 19 2020
STATUS
approved