A227652 Perfect powers which are the product of distinct factorials.

1, 144, 518400, 2073600, 406425600, 3657830400, 14631321600, 58525286400, 526727577600, 2106910310400, 13168189440000, 52672757760000, 210691031040000, 842764124160000, 1769804660736000, 1896219279360000, 7584877117440000, 30339508469760000

Offset: 1

Author

Giovanni Resta, Jul 19 2013

Keywords

• nonn

Comments

The first occurrences of nontrivial 2nd, 3rd,..., 6th powers are 3!*4!, 4!*7!*8!*9!, 2!*3!*4!*6!*7! * 13!*14!*15!*16!, 27!*26!*25!*24!*23! * 16!*15!*14!*12!*11!*9!*8!*3!*2! and 78!*77!*76!*75!*74!*73! * 37!*35!*34!*33!*32!*31! * 21!*20!*19!*14!*13! * 12!*9!*8!*7!*3!.

Examples

			14631321600 = 120960^2 = 8! * 9!.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..2132 (terms < 10^100)
• Giovanni Resta, Decompositions for a(1)-a(2132)

Crossrefs

Cf. A051761.

Programs

Mathematica

seqUpto[ub_] := Block[{ric, L={1}}, ric[m_, fr_] := Block[{mm, k = fr}, If[GCD @@ (Last /@ FactorInteger[m]) > 1, AppendTo[L, m]]; While[(mm = m*k!) <= ub, ric[mm, ++k]]]; ric[1, 2]; Union@L]; seqUpto[10^20] (* Giovanni Resta, Jul 19 2013 *)