A066729 a(n) = Product_{d|n, d<n} d if n is composite, n otherwise.

1, 2, 3, 2, 5, 6, 7, 8, 3, 10, 11, 144, 13, 14, 15, 64, 17, 324, 19, 400, 21, 22, 23, 13824, 5, 26, 27, 784, 29, 27000, 31, 1024, 33, 34, 35, 279936, 37, 38, 39, 64000, 41, 74088, 43, 1936, 2025, 46, 47, 5308416, 7, 2500, 51, 2704, 53, 157464, 55, 175616, 57

Offset

1,2

Comments

a(n) = n if n is prime, otherwise a(n) = A007956(n);

a(A084116(n)) = A084116(n).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = n^c(n) * ( Product_{d|n, d<n} d )^(1-c(n)), where c is the prime characteristic (A010051). - Wesley Ivan Hurt, Jan 10 2021

Mathematica

a[1] = 1; a[n_ /; PrimeQ[n]] := n; a[n_] := Times @@ Most[Divisors[n]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, May 28 2015 *)
Table[If[CompositeQ[n], Times@@Most[Divisors[n]], n], {n, 60}] (* Harvey P. Dale, Jun 24 2016 *)

Prog

(Haskell)
a066729 n = if pds == [1] then n else product pds
            where pds = a027751_row n
-- Reinhard Zumkeller, Jul 31 2014
(PARI) a(n) = my(pd = vecprod(divisors(n))); if (isprime(n), pd, pd/n); \\ Michel Marcus, Jan 09 2021

Crossrefs

Cf. A002033, A006881, A030514, A000040.

Cf. A027751, A007956, A084116, A010051.

Sequence in context: A366765 A361253 A097448 * A241592 A211506 A182880

Adjacent sequences: A066726 A066727 A066728 * A066730 A066731 A066732

Keyword

nonn,nice

Author

Reinhard Zumkeller, Jan 15 2002

Extensions

Revised and data corrected by Reinhard Zumkeller, Jul 31 2014

Status

approved