A306507 a(n) = gcd(n!^2+1, sigma(n!)), where sigma() denotes the sum of the divisors.

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.

Links

Table of n, a(n) for n=1..85.

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

Cf. A000203, A020549, A062569.

Sequence in context: A058018 A037283 A278634 * A094709 A236231 A040181

Adjacent sequences: A306504 A306505 A306506 * A306508 A306509 A306510

Keyword

nonn

Author

Daoudi Rédoane, Feb 20 2019

Extensions

More terms from Michel Marcus, Feb 20 2019

Status

approved