A056190 a(n) = Sum_{d|n and gcd(d, n/d)=1} binomial(n,d).

1, 3, 4, 5, 6, 42, 8, 9, 10, 308, 12, 728, 14, 3538, 3474, 17, 18, 48792, 20, 20370, 117632, 705686, 24, 737520, 26, 10400952, 28, 1204544, 30, 185903342, 32, 33, 193542210, 2333606816, 7049188, 94202222, 38, 35345264542, 8122434623

Offset: 1

Author

Labos Elemer, Aug 02 2000

Keywords

• nonn

Examples

			n=100 has 9 divisors of which {1,4,25,100} are unitary, so a(100) = 100 + 3921225 + 242519269720337121015504 + 1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A056045.

Programs

Maple

a:= n-> add(`if`(igcd(d, n/d)=1, binomial(n, d), 0),
                      d=numtheory[divisors](n)):
seq(a(n), n=1..40);  # Alois P. Heinz, Aug 25 2019

Mathematica

a[n_] := Total[Binomial[n, Select[Divisors[n], CoprimeQ[#, n/#] &]]]; Array[a, 40] (* Amiram Eldar, Jul 28 2024 *)

PARI

a(n) = sumdiv(n, d, if (gcd(d, n/d)==1, binomial(n, d))); \\ Michel Marcus, Aug 25 2019

Formula

a(n) = A056045(n) for squarefree n, when all divisors are unitary.