OFFSET
1,2
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!.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..2132 (terms < 10^100)
Giovanni Resta, Decompositions for a(1)-a(2132)
EXAMPLE
14631321600 = 120960^2 = 8! * 9!.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Giovanni Resta, Jul 19 2013
STATUS
approved