login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A221583 A sum over partitions (q=18), see first comment. 8
1, 17, 323, 5814, 104958, 1889227, 34011900, 612213877, 11019954438, 198359179578, 3570467115834, 64268408079198, 1156831379431973, 20822964829665048, 374813367546080412, 6746640615829343087, 121439531095946141922, 2185911559727028566514 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Set q=18 and f(m)=q^(m-1)*(q-1), then a(n) is the sum over all partitions P of n over all products prod(k=1..L, f(m_k) ) where L is the number of different parts in the partition P=[p_1^m_1, p_2^m_2, ..., p_L^m_L].

Setting q to a prime power gives the sequence "Number of conjugacy classes in GL(n,q)":

q=3: A006952, q=4: A049314, q=5: A049315, q=7: A049316, q=8: A182603,

q=9: A182604, q=11: A182605, q=13: A182606, q=16: A182607, q=17: A182608,

q=19: A182609, q=23: A182610, q=25: A182611, q=27: A182612.

Sequences where q is not a prime power are:

q=6: A221578, q=10: A221579, q=12: A221580,

q=14: A221581, q=15: A221582, q=18: A221583, q=20: A221584.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

MAPLE

with(numtheory):

b:= proc(n) b(n):= add(phi(d)*18^(n/d), d=divisors(n))/n-1 end:

a:= proc(n) a(n):= `if`(n=0, 1,

       add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Feb 03 2013

MATHEMATICA

b[n_] := Sum[EulerPhi[d]*18^(n/d), {d, Divisors[n]}]/n-1; a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*b[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Feb 17 2014, after Alois P. Heinz *)

PROG

(PARI)

N=66; x='x+O('x^N);

gf=prod(n=1, N, (1-x^n)/(1-18*x^n)  );

v=Vec(gf)

CROSSREFS

Sequence in context: A089571 A196455 A217960 * A091464 A015693 A029535

Adjacent sequences:  A221580 A221581 A221582 * A221584 A221585 A221586

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jan 20 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 18 17:56 EST 2017. Contains 294894 sequences.