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A225938 Number of conjugacy classes in Chevalley group E_8(q) as q runs through the prime powers (A246655).

%I A225938 #17 Mar 24 2020 11:15:22
%S A225938 1156,12825,97154,519071,6906102,19543486,49150839,238045722,
%T A225938 889575240,4600759094,7439557452,17980383618,82034207430,159213167411,
%U A225938 293713437009,518754968088,882274298862,1136129443366,3612770425152,8189556710532,11973138177210,24340206797502
%N A225938 Number of conjugacy classes in Chevalley group E_8(q) as q runs through the prime powers (A246655).
%H A225938 Eric M. Schmidt, <a href="/A225938/b225938.txt">Table of n, a(n) for n = 1..1000</a>
%H A225938 Frank Luebeck, <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/chev/nrclasses/nrclasses.html">Numbers of Conjugacy Classes in Finite Groups of Lie Type</a>.
%H A225938 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A225938 Let q be the n-th prime power. Then a(n) is
%F A225938 q^8 + q^7 + 2q^6 + 3q^5 +  9q^4 + 14q^3 + 32q^2 + 47q +  70, q==0(mod 2);
%F A225938 q^8 + q^7 + 2q^6 + 3q^5 + 10q^4 + 16q^3 + 39q^2 + 65q + 102, q==0(mod 3);
%F A225938 q^8 + q^7 + 2q^6 + 3q^5 + 10q^4 + 16q^3 + 40q^2 + 67q + 111, q==0(mod 5);
%F A225938 q^8 + q^7 + 2q^6 + 3q^5 + 10q^4 + 16q^3 + 40q^2 + 67q + 112, otherwise.
%p A225938 A225938 := proc(n)
%p A225938     local q ;
%p A225938     q := A246655(n) ;
%p A225938     if modp(q,2) = 0 then
%p A225938         q^8 + q^7 + 2*q^6 + 3*q^5 +  9*q^4 + 14*q^3 + 32*q^2 + 47*q +  70;
%p A225938     elif modp(q,3) = 0 then
%p A225938         q^8 + q^7 + 2*q^6 + 3*q^5 + 10*q^4 + 16*q^3 + 39*q^2 + 65*q + 102 ;
%p A225938     elif modp(q,5) = 0 then
%p A225938         q^8 + q^7 + 2*q^6 + 3*q^5 + 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 111 ;
%p A225938     else
%p A225938         q^8 + q^7 + 2*q^6 + 3*q^5 + 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 112 ;
%p A225938     end if;
%p A225938 end proc: # _R. J. Mathar_, Jan 09 2017
%t A225938 qmax = 100;
%t A225938 Reap[For[q = 2, q < qmax, q++, If[PrimePowerQ[q], cc = q^8 + q^7 + 2 q^6 + 3 q^5 + Which[Mod[q, 2] == 0, 9 q^4 + 14 q^3 + 32 q^2 + 47 q + 70, Mod[q, 3] == 0, 10 q^4 + 16 q^3 + 39 q^2 + 65 q + 102, Mod[q, 5] == 0, 10 q^4 + 16 q^3 + 40 q^2 + 67 q + 111, True, 10 q^4 + 16 q^3 + 40 q^2 + 67 q + 112]; Sow[cc]]]][[2, 1]] (* _Jean-François Alcover_, Mar 24 2020 *)
%o A225938 (Sage) def A225938(q) : return q^8 + q^7 + 2*q^6 + 3*q^5 + (9*q^4 + 14*q^3 + 32*q^2 + 47*q + 70 if q%2==0 else 10*q^4 + 16*q^3 + 39*q^2 + 65*q + 102 if q%3==0 else 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 111 if q%5==0 else 10*q^4 + 16*q^3 + 40*q^2 + 67*q + 112)
%Y A225938 Cf. A188161, A224790, A225928-A225937.
%K A225938 nonn
%O A225938 1,1
%A A225938 _Eric M. Schmidt_, May 21 2013