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

1,2

Comments

All terms are powers of 2.

Links

Table of n, a(n) for n=1..59.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A000188.

Sequence in context: A095061 A184233 A356386 * A117215 A011173 A162943

Adjacent sequences: A055074 A055075 A055076 * A055078 A055079 A055080

Keyword

nonn

Author

Labos Elemer, Jun 13 2000

Status

approved