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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.

%I A271503 #28 Nov 18 2022 08:33:16
%S A271503 1,1,2,6,2,120,2,210,2,1890,2,83160,2,270270,2,4054050,2,275675400,2,
%T A271503 1309458150,2,27498621150,2,2529873145800,2,15811707161250,2,
%U A271503 426916093353750,2,49522266829035000,2,383797567925021250,2,12665319741525701250,2
%N A271503 a(1) = 1; thereafter a(n) is the product of all 0 < m < n for which a(m) divides n.
%H A271503 Chai Wah Wu, <a href="/A271503/b271503.txt">Table of n, a(n) for n = 1..809</a> (n = 1..100 from Peter Kagey)
%F A271503 a(2n + 1) = 2 for all n > 1.
%F A271503 a(n) is even for all n > 2.
%e A271503 a(1) = 1 by definition
%e A271503 a(2) = 1 because a(1) divides 2.
%e A271503 a(3) = 1 * 2 = 2 because a(1) and a(2) divide 3.
%e A271503 a(4) = 1 * 2 * 3 = 6 because a(1), a(2), and a(3) divide 4.
%e A271503 a(5) = 1 * 2 = 2 because a(1) and a(2) divide 5.
%t A271503 a = {1}; Do[AppendTo[a, Times @@ Flatten@ Position[a, m_ /; Divisible[n, m]]], {n, 2, 35}]; a (* _Michael De Vlieger_, Apr 09 2016 *)
%o A271503 (Python)
%o A271503 from itertools import count, islice
%o A271503 from math import prod
%o A271503 from sympy import divisors
%o A271503 def A271503_gen(): # generator of terms
%o A271503     A271503_dict = {1:1}
%o A271503     yield 1
%o A271503     for n in count(2):
%o A271503         yield (s:=prod(A271503_dict.get(d,1) for d in divisors(n,generator=True)))
%o A271503         A271503_dict[s] = A271503_dict.get(s,1)*n
%o A271503 A271503_list = list(islice(A271503_gen(),40)) # _Chai Wah Wu_, Nov 17 2022
%Y A271503 Cf. A269347, A271504.
%K A271503 nonn
%O A271503 1,3
%A A271503 _Peter Kagey_, Apr 08 2016