A121773 Number of n-bead necklaces with n+1 colors for n>0, with a(0)=1.

1, 2, 6, 24, 165, 1560, 19684, 299600, 5381685, 111111340, 2593758618, 67546215528, 1941507500933, 61054982558024, 2085209014017960, 76861433640597376, 3041324492665174641, 128583032925805678368, 5784852794346334629910, 275941052631578947368440

Offset: 0

Author

Paul D. Hanna, Aug 20 2006

Keywords

• nonn

Links

• Stefano Spezia, Table of n, a(n) for n = 0..350

Crossrefs

Cf. A121774, A056665.

Programs

Mathematica

a[0] = 1; a[n_] := DivisorSum[n, (n+1)^# * EulerPhi[n/#] &] / n; Array[a, 20, 0] (* Amiram Eldar, Aug 15 2023 *)

PARI

a(n)=if(n==0,1,(1/n)*sumdiv(n,d,eulerphi(n/d)*(n+1)^d))

Formula

a(n) = (1/n)*Sum_{d|n} phi(n/d)*(n+1)^d, for n>0, with a(0)=1.

a(n) is divisible by (n+1); a(n)/(n+1) = A121774(n).

Extensions

a(18)-a(19) from Amiram Eldar, Aug 15 2023