login
A306507
a(n) = gcd(n!^2+1, sigma(n!)), where sigma() denotes the sum of the divisors.
0
1, 1, 1, 1, 1, 13, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 61, 1, 1, 1, 1, 1, 1, 1, 1, 61, 1, 1, 1, 193, 1, 1, 1, 757, 61, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 109, 1, 1, 1, 181, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 113
OFFSET
1,6
COMMENTS
A sequence that produces primes.
A counterexample is found at n=7880, here the gcd is 380927609 = 15761*24169.
Interesting properties may be found in this sequence, for example many primes are 2n+1.
FORMULA
a(n) = gcd(A020549(n), A062569(n)).
MATHEMATICA
Table[GCD[(n!)^2+1, DivisorSigma[1, n!]], {n, 90}] (* Harvey P. Dale, Jun 03 2021 *)
PROG
(PARI) a(n) = gcd(n!^2+1, sigma(n!)); \\ Michel Marcus, Feb 20 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Daoudi RĂ©doane, Feb 20 2019
EXTENSIONS
More terms from Michel Marcus, Feb 20 2019
STATUS
approved