A389555 Perfect squares which are the product of three distinct factorials.

144, 518400, 2073600, 406425600, 3657830400, 14631321600, 13168189440000, 27360196043587190784000000, 4554487674199698126667776000000, 213084438530037396675027900825600000000, 96239054803332819234934250538241779302400000000, 384956219213331276939737002152967117209600000000

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..69

Example

From Michael De Vlieger, Oct 11 2025: (Start)
Table of n, a(n), n = 1..10, showing 3 factorial factors for each:
                                               Factorial
 n                                       a(n)  Factors
---------------------------------------------------------
 1                                       144   1!  3!  4!
 2                                    518400   3!  5!  6!
 3                                   2073600   4!  5!  6!
 4                                 406425600   2!  7!  8!
 5                                3657830400   2!  7!  9!
 6                               14631321600   1!  8!  9!
 7                            13168189440000   6!  7! 10!
 8                27360196043587190784000000   1! 15! 16!
 9           4554487674199698126667776000000   2! 17! 18!
10   213084438530037396675027900825600000000   6! 19! 20! (End)

Mathematica

Union@ Select[Times @@@ Subsets[Array[Factorial, 24], {3}], GCD @@ FactorInteger[#][[;; , -1]] > 1 &] (* Michael De Vlieger, Oct 11 2025 *)

Crossrefs

Cf. A388851, A389553.

Subset of A227652.

Sequence in context: A033514 A086778 A227652 * A159436 A318197 A362214

Adjacent sequences: A389552 A389553 A389554 * A389556 A389557 A389558

Keyword

nonn

Author

Paolo Xausa, Oct 11 2025

Status

approved