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A066729 a(n) = Product_{d|n, d<n} d if n is composite, n otherwise. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A331737 A135875 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

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Last modified December 1 08:44 EST 2021. Contains 349426 sequences. (Running on oeis4.)