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A054631
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Triangle read by rows: row n (n>=1) contains the numbers T(n,k) = sum_{d|n} phi(d)*k^(n/d)/n, for k=1..n.
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6
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1, 1, 3, 1, 4, 11, 1, 6, 24, 70, 1, 8, 51, 208, 629, 1, 14, 130, 700, 2635, 7826, 1, 20, 315, 2344, 11165, 39996, 117655, 1, 36, 834, 8230, 48915, 210126, 720916, 2097684, 1, 60, 2195, 29144, 217045, 1119796, 4483815, 14913200, 43046889
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..45.
Index entries for sequences related to necklaces
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EXAMPLE
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1;
1,3; - A000217
1,4,11; - A006527
1,6,24,70; - A006528
1,8,51,208,629; - A054620
1,14,130,700,2635,7826; - A006565
1,20,315,2344,11165,39996,117655; - A054621
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MAPLE
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A054631 := proc(n, k) add( numtheory[phi](d)*k^(n/d), d=numtheory[divisors](n) ) ; %/n ; end proc: # R. J. Mathar, Aug 30 2011
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MATHEMATICA
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Needs["Combinatorica`"]; Table[Table[NumberOfNecklaces[n, k, Cyclic], {k, 1, n}], {n, 1, 8}] //Grid (* after code by T.D. Noe in A027671, Geoffrey Critzer, Oct 07 2012 *)
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CROSSREFS
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Cf. A054630, A054618, A054619. Lower triangle of A075195.
Sequence in context: A081720 A137405 A121922 * A180063 A125077 A065253
Adjacent sequences: A054628 A054629 A054630 * A054632 A054633 A054634
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane, Apr 16 2000, revised Mar 21 2007
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STATUS
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approved
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