A271503 a(1) = 1; thereafter a(n) is the product of all 0 < m < n for which a(m) divides n.

1, 1, 2, 6, 2, 120, 2, 210, 2, 1890, 2, 83160, 2, 270270, 2, 4054050, 2, 275675400, 2, 1309458150, 2, 27498621150, 2, 2529873145800, 2, 15811707161250, 2, 426916093353750, 2, 49522266829035000, 2, 383797567925021250, 2, 12665319741525701250, 2

Offset: 1

Author

Peter Kagey, Apr 08 2016

Keywords

• nonn

Examples

			a(1) = 1 by definition
a(2) = 1 because a(1) divides 2.
a(3) = 1 * 2 = 2 because a(1) and a(2) divide 3.
a(4) = 1 * 2 * 3 = 6 because a(1), a(2), and a(3) divide 4.
a(5) = 1 * 2 = 2 because a(1) and a(2) divide 5.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..809 (n = 1..100 from Peter Kagey)

Crossrefs

Cf. A269347, A271504.

Programs

Mathematica

a = {1}; Do[AppendTo[a, Times @@ Flatten@ Position[a, m_ /; Divisible[n, m]]], {n, 2, 35}]; a (* Michael De Vlieger, Apr 09 2016 *)

Python

from itertools import count, islice
from math import prod
from sympy import divisors
def A271503_gen(): # generator of terms
    A271503_dict = {1:1}
    yield 1
    for n in count(2):
        yield (s:=prod(A271503_dict.get(d,1) for d in divisors(n,generator=True)))
        A271503_dict[s] = A271503_dict.get(s,1)*n
A271503_list = list(islice(A271503_gen(),40)) # Chai Wah Wu, Nov 17 2022

Formula

a(2n + 1) = 2 for all n > 1.

a(n) is even for all n > 2.