A208190
Number of distinct 5-colored necklaces with n beads per color.
Original entry on oeis.org
1, 24, 11352, 11211216, 15277017432, 24934429725024, 45695805591924048, 90784545100668913392, 191417861328837588057432, 422458626725600682518100816, 966695515158024410709527456352, 2277925055026596846727033776223440, 5499697195473757755182168765034005328
Offset: 0
a(0) = 1: the empty necklace.
a(1) = 24: {01234, 01243, ..., 04321}.
-
with(numtheory):
a:= n-> `if`(n=0, 1, add(phi(n/d) * (5*d)!/(d!^5 *5*n), d=divisors(n))):
seq(a(n), n=0..14);
A208191
Number of distinct 6-colored necklaces with n beads per color.
Original entry on oeis.org
1, 120, 623760, 7623616080, 135277939358160, 2961088201992945120, 74171603795480180204640, 2041012695880532470281654960, 60192781171721237282811209918160, 1872173374511564116503341160073744080, 60735890264793885272652711347090416733760
Offset: 0
a(0) = 1: the empty necklace.
a(1) = 120: {012345, 012354, ..., 054321}.
-
with(numtheory):
a:= n-> `if`(n=0, 1, add(phi(n/d) *(6*d)!/(d!^6 *6*n), d=divisors(n))):
seq(a(n), n=0..12);
A208192
Number of distinct 7-colored necklaces with n beads per color.
Original entry on oeis.org
1, 720, 48648960, 8690922240480, 2374127830286012160, 823940558733748910598720, 333504309246734399617946903040, 150277870737901828652705825755721760, 73288704867601350013562616043249358012160, 37980016035292737119901943600678905519608160480
Offset: 0
a(0) = 1: the empty necklace.
a(1) = 720: {0123456, 0123465, ..., 0654321}.
-
with(numtheory):
a:= n-> `if`(n=0, 1, add(phi(n/d) *(7*d)!/(d!^7 *7*n), d=divisors(n))):
seq(a(n), n=0..12);
A208193
Number of distinct 8-colored necklaces with n beads per color.
Original entry on oeis.org
1, 5040, 5108105520, 15391623287043360, 74701932179186551241520, 474389544274867071519255599040, 3581026866351385580856518554063502880, 30495546426686489361833408314854897254404320, 283839436431731355577562936415156522873876247241520
Offset: 0
a(0) = 1: the empty necklace.
a(1) = 5040: {01234567, 01234576, ..., 07654321}.
-
with(numtheory):
a:= n-> `if`(n=0, 1, add(phi(n/d) *(8*d)!/(d!^8 *8*n), d=divisors(n))):
seq(a(n), n=0..10);
A252765
Number of distinct n-colored necklaces with n beads per color.
Original entry on oeis.org
1, 1, 2, 188, 3941598, 24934429725024, 74171603795480180204640, 150277870737901828652705825755721760, 283839436431731355577562936415156522873876247241520, 655934428473920614716696820356119117524334608980167506174657536026880
Offset: 0
-
with(numtheory):
a:= n-> `if`(n=0, 1, add(phi(n/d)*(n*d)!/(d!^n*n^2), d=divisors(n))):
seq(a(n), n=0..10);
-
a[n_] := If[n == 0, 1, DivisorSum[n, EulerPhi[n/#]*(n*#)!/(#!^n*n^2)&]];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Mar 25 2017, translated from Maple *)
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