A271504 -id:A271504 - cp's OEIS frontend

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

Peter Kagey, Apr 08 2016

nonn

			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.

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

Cf. A269347, A271504.

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

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

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

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

A271774 a(1) = 1, then a(n) is the maximum of all 0 < m < n for which a(m) divides n.

Original entry on oeis.org

1, 1, 2, 3, 2, 5, 2, 7, 4, 7, 2, 11, 2, 13, 6, 13, 2, 17, 2, 19, 10, 19, 2, 23, 6, 23, 4, 27, 2, 29, 2, 31, 12, 31, 10, 33, 2, 37, 16, 37, 2, 41, 2, 43, 6, 43, 2, 47, 10, 49, 18, 47, 2, 53, 12, 53, 22, 53, 2, 59, 2, 61, 10, 61, 16, 61, 2, 67, 26, 67, 2, 71, 2

Offset: 1

Peter Kagey, Apr 14 2016

nonn

If n is an odd prime, then a(n) = 2 and a(n+1) = n. All n for which a(n) = 2 are odd primes. - Robert Israel, Apr 14 2016

			a(1) = 1 by definition.
a(2) = 1 because a(1) divides 2.
a(3) = 2 because a(2) divides 3.
a(4) = 3 because a(3) divides 4.
a(5) = 2 because a(2) divides 5.
a(6) = 5 because a(5) divides 6.
a(7) = 2 because a(2) divides 7.
a(8) = 7 because a(7) divides 8.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A088167, A269347, A271503, A271504, A271773.

A:= proc(n) option remember; local m;
    for m from n-1 by -1 do
      if n mod A(m) = 0 then return m fi
    od
end proc:
A(1):= 1:
seq(A(i),i=1..100); # Robert Israel, Apr 14 2016

a[1] = 1; a[n_] := a[n] = Block[{m = n - 1}, While[Mod[n, a[m]] > 0, m--]; m]; Array[a, 100] (* Giovanni Resta, Apr 14 2016 *)

cp's OEIS Frontend

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

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