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A271503
a(1) = 1; thereafter a(n) is the product of all 0 < m < n for which a(m) divides n.
3
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
Sequence in context: A005729 A271504 A086660 * A102068 A351709 A188733
KEYWORD
nonn
AUTHOR
Peter Kagey, Apr 08 2016
STATUS
approved