A055077 Multiplicity of Max{gcd(d, n!/d)} when d runs over the divisors of n!.

1, 2, 4, 4, 8, 2, 4, 8, 8, 2, 4, 8, 16, 16, 16, 16, 32, 16, 32, 16, 64, 64, 128, 32, 32, 32, 64, 32, 64, 32, 64, 128, 512, 128, 128, 128, 256, 256, 256, 256, 512, 1024, 2048, 1024, 512, 128, 256, 128, 128, 256, 1024, 512, 1024, 256, 1024, 4096, 16384, 4096, 8192

Offset: 1

Author

Labos Elemer, Jun 13 2000

Keywords

• nonn

Comments

All terms are powers of 2.

Examples

			n=5, 5!=120, the set of gcd(d, 120/d) values for the 16 divisors of 120 is {1,2,1,2,1,2,1,2,2,1,2,1,2,1,2,1}. The maximum is 2 and it occurs 8 times, so a(5)=8.
		

Crossrefs

Cf. A000188.

Programs

Mathematica

Table[Count[#, Max@ #] &@ Map[GCD[#, m/#] &, Divisors[m]], {m, Range[30]!}] (* Michael De Vlieger, Oct 06 2019 *)

Formula

It appears that a(n) = 2^A055460(n). - Joerg Arndt, Oct 06 2019