A061860 Variant of A061417.

1, 2, 4, 11, 28, 152, 726, 5268, 40438, 365944, 3628810, 39974466, 479001612, 6228256404, 87178339984, 1307706805928, 20922789888016, 355688409760972, 6402373705728018, 121645133931170028, 2432902008232456692

Offset: 0

Author

Antti Karttunen, May 11 2001

Keywords

• nonn

Comments

Does this count some variety of necklaces?

Links

• G. C. Greubel, Table of n, a(n) for n = 0..445

Crossrefs

A061860[p] = A061417[p] = (p-1)!+(p-1) for all prime p's.

Programs

Maple

[seq(A061860(j),j=1..40)]; with(numtheory); A061860 := proc(n) local d,s; s := 0; for d in divisors(n) do s := s + phi(n/d)*(binomial(n,d))*(d!); od; RETURN(s/n); end;

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#] Binomial[n, #] (#!)&]/n; Array[a, 25] (* Jean-François Alcover, Mar 06 2016 *)

Formula

a(n) = (1/n)*Sum_{d|n} phi(n/d)*C(n, d)*(d!).