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A054631 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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..45.

Index entries for sequences related to necklaces

EXAMPLE

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)

MAPLE

A054631 := proc(n, k) add( numtheory[phi](d)*k^(n/d), d=numtheory[divisors](n) ) ;  %/n ; end proc: # R. J. Mathar, Aug 30 2011

MATHEMATICA

Needs["Combinatorica`"]; Table[Table[NumberOfNecklaces[n, k, Cyclic], {k, 1, n}], {n, 1, 8}] //Grid (* Geoffrey Critzer, Oct 07 2012, after code by T. D. Noe in A027671 *)

t[n_, k_] := Sum[EulerPhi[d]*k^(n/d)/n, {d, Divisors[n]}]; Table[t[n, k], {n, 1, 9}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Jan 20 2014 *)

CROSSREFS

Cf. A054630, A054618, A054619. Lower triangle of A075195.

Sequence in context: A301701 A262078 A121922 * A180063 A125077 A065253

Adjacent sequences:  A054628 A054629 A054630 * A054632 A054633 A054634

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Apr 16 2000, revised Mar 21 2007

STATUS

approved

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Last modified November 17 05:59 EST 2018. Contains 317275 sequences. (Running on oeis4.)