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

1,3

Links

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

Formula

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

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A269347, A271504.

Sequence in context: A005729 A271504 A086660 * A102068 A351709 A188733

Adjacent sequences: A271500 A271501 A271502 * A271504 A271505 A271506

Keyword

nonn

Author

Peter Kagey, Apr 08 2016

Status

approved