A271503 - OEIS

%I #28 Nov 18 2022 08:33:16

%S 1,1,2,6,2,120,2,210,2,1890,2,83160,2,270270,2,4054050,2,275675400,2,

%T 1309458150,2,27498621150,2,2529873145800,2,15811707161250,2,

%U 426916093353750,2,49522266829035000,2,383797567925021250,2,12665319741525701250,2

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

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

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

%e a(1) = 1 by definition

%e a(2) = 1 because a(1) divides 2.

%e a(3) = 1 * 2 = 2 because a(1) and a(2) divide 3.

%e a(4) = 1 * 2 * 3 = 6 because a(1), a(2), and a(3) divide 4.

%e a(5) = 1 * 2 = 2 because a(1) and a(2) divide 5.

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

%o (Python)

%o from itertools import count, islice

%o from math import prod

%o from sympy import divisors

%o def A271503_gen(): # generator of terms

%o     A271503_dict = {1:1}

%o     yield 1

%o     for n in count(2):

%o         yield (s:=prod(A271503_dict.get(d,1) for d in divisors(n,generator=True)))

%o         A271503_dict[s] = A271503_dict.get(s,1)*n

%o A271503_list = list(islice(A271503_gen(),40)) # _Chai Wah Wu_, Nov 17 2022

%Y Cf. A269347, A271504.

%K nonn

%O 1,3

%A _Peter Kagey_, Apr 08 2016