OFFSET
0,3
COMMENTS
a(2372) has 1001 decimal digits. - Michael De Vlieger, Jul 14 2017
Also the squarefree kernel of the cumulative product of n^n/n!. - Peter Luschny, Dec 21 2019
Conjecture: the few odd values belong to A070826. - Bill McEachen, Jun 24 2023
And their indices appear to be A007053. - Michel Marcus, Jul 01 2023
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..2371
FORMULA
a(n) = radical(hyperfactorial(n)/superfactorial(n)) = A007947(A002109(n)/ A000178(n)) for n >= 0. - Peter Luschny, Dec 21 2019
EXAMPLE
a(7) = 105 because lcm(1, 7, 21, 35) = 105 is already squarefree.
a(0) = 1 because n^n/n! = 1 for the integer n = 0. - Peter Luschny, Dec 21 2019
MAPLE
h := n -> mul(k^k/factorial(k), k=0..n):
rad := n -> mul(k, k = numtheory[factorset](n)):
seq(rad(h(n)), n=0..31); # Peter Luschny, Dec 21 2019
MATHEMATICA
Table[Apply[Times, FactorInteger[Product[k^(2 k - 1 - n), {k, n}]][[All, 1]]], {n, 0, 31}] (* or *)
Table[Apply[Times, FactorInteger[Apply[LCM, Range@ n]/n][[All, 1]]], {n, 1, 32}] (* Michael De Vlieger, Jul 14 2017 *)
PROG
(Haskell)
a056606 = a007947 . a001142 -- Reinhard Zumkeller, Mar 21 2015
(PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
a(n) = rad(lcm(vector(n+1, k, binomial(n, k-1)))); \\ Michel Marcus, Jun 24 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 07 2000
EXTENSIONS
Extended with a(0) = 1 by Peter Luschny, Dec 21 2019
STATUS
approved