A271530 a(1) = 1; thereafter a(n) is the product of all 0 < m < n for which n == a(m) (mod m).

1, 1, 2, 1, 24, 1, 12, 3, 40, 1, 480, 7, 432, 15, 28, 13, 24, 11, 40320, 3, 1520, 9, 120, 85, 48, 21, 16, 345, 1452971520, 1, 8553600, 3, 56, 5, 44544, 1, 1161216, 3, 340, 13167, 155040, 13, 130636800, 15, 4736, 1, 36167040, 1075, 66960, 63, 40480, 1, 27456

Offset: 1

Author

Peter Kagey, Apr 09 2016

Keywords

• nonn

Examples

			a(1) = 1 by definition.
a(2) = 1, because 2 == a(1) (mod 1);
a(3) = 2, because 3 == a(1) (mod 1), and 3 == a(2) (mod 2): 1 * 2 = 2;
a(4) = 1, because 4 == a(1) (mod 1);
a(5) = 24, because 5 == k (mod k) for 0 < k < 5: 1 * 2 * 3 * 4 = 24.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A269423, A271531.

Programs

Mathematica

a = {1}; Do[AppendTo[a, Times @@ Flatten@ Position[MapIndexed[Mod[n, First@ #2] == Mod[#1, First@ #2] &, a], True]], {n, 2, 53}]; a (* Michael De Vlieger, Apr 09 2016 *)