A069785 a(n) = A061680(n!).

1, 1, 1, 1, 1, 15, 15, 3, 5, 135, 135, 99, 99, 9, 63, 21, 21, 459, 459, 135, 19, 15, 15, 15, 21, 189, 189, 585, 585, 18225, 18225, 675, 15, 135, 891, 8505, 25515, 81, 81, 7695, 7695, 1575, 1575, 4725, 6615, 40635, 40635, 945, 1215, 3645, 3645, 151875, 151875

Offset: 1

Author

Labos Elemer, Apr 09 2002

Keywords

• easy
• nonn

Examples

			Observe cases when consecutive terms are equal: n={1,2,3,4,6,10,...,78,80,82,88,96}.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000142, A061680, A061701, A048691, A069780, A069781, A069782, A069783, A069784.

Programs

Mathematica

a[n_] := Module[{e = FactorInteger[n!][[;;, 2]]}, GCD[Times @@ (2*e+1), Times @@ (e+1)]]; Array[a, 100] (* Amiram Eldar, Dec 02 2023 *)

PARI

a(n) = {my(e = factor(n!)[,2]); gcd(vecprod(apply(x -> 2*x+1, e)), vecprod(apply(x -> x+1, e)));} \\ Amiram Eldar, Dec 02 2023

Formula

a(n) = A061680(A000142(n)). - Amiram Eldar, Dec 02 2023