A158851 a(n) = lcm(1,2,3,...,n) mod (n+1).

1, 2, 2, 2, 0, 4, 4, 3, 0, 1, 0, 4, 0, 0, 8, 5, 0, 14, 0, 0, 0, 15, 0, 5, 0, 18, 0, 1, 0, 20, 16, 0, 0, 0, 0, 2, 0, 0, 0, 15, 0, 15, 0, 0, 0, 8, 0, 21, 0, 0, 0, 29, 0, 0, 0, 0, 0, 21, 0, 16, 0, 0, 32, 0, 0, 29, 0, 0, 0, 23, 0, 22, 0, 0, 0, 0, 0, 30, 0, 54, 0, 71, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 7, 0

Offset: 1

Author

Leroy Quet, Mar 28 2009

Keywords

• nonn

Comments

If n+1 is not a power of a prime, then a(n) = 0.

If n+1 = p^m, p = prime, then p^(m-1) (= (n+1)/p) divides a(n), but p^m (= n+1) does not divide a(n).

Examples

			a(6) = lcm(1,2,3,4,5,6) mod (6+1) = 60 mod 7 = 4.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003418.

Programs

GAP

List([1..100],n->Lcm([1..n]) mod (n+1)); # Muniru A Asiru, Mar 06 2018

Magma

[Lcm([1..n]) mod (n+1): n in [1..100]]; // Vincenzo Librandi, Mar 07 2018

Maple

a := proc (n) options operator, arrow: `mod`(lcm(seq(j, j = 1 .. n)), n+1) end proc: seq(a(n), n = 1 .. 100); # Emeric Deutsch, Apr 03 2009

Mathematica

Array[Mod[LCM @@ Range@ #, # + 1] &, 97] (* Michael De Vlieger, Mar 04 2018 *)

PARI

a(n) = lcm(vector(n, k, k)) % (n+1); \\ Michel Marcus, Mar 06 2018

Formula

a(2^n-1) = 2^(n-1). - Thomas Ordowski, Sep 18 2018

Extensions

More terms from Emeric Deutsch, Apr 03 2009