%I #13 Aug 20 2024 23:52:44
%S 0,211341312,20560831566912,67802350642790400,35817806390625000000,
%T 450782974156649555296512,19045158721552047314829312,
%U 516964372056378442547769600,143027806714329275383382337600,15411735887347424297802263464512
%N q^12*(q^8+q^4+1)*(q^6-1)*(q^2-1) as q runs through the prime powers A000961.
%C For n>1, the order of the twisted Chevalley group (3)D_4(q).
%D R. W. Carter, Simple Groups of Lie Type, Wiley 1972, Chap. 14, p. 262.
%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
%o (Python)
%o from sympy import primepi, integer_nthroot
%o def A359129(n):
%o def f(x): return int(n-2+x-sum(primepi(integer_nthroot(x,k)[0]) for k in range(1,x.bit_length())))
%o kmin, kmax = 1,2
%o while f(kmax) >= kmax:
%o kmax <<= 1
%o while True:
%o kmid = kmax+kmin>>1
%o if f(kmid) < kmid:
%o kmax = kmid
%o else:
%o kmin = kmid
%o if kmax-kmin <= 1:
%o break
%o return ((m:=kmax**2)*(m*(m*(m*(m*(m*(m*(m-1)+1)-2)+2)-2)+1)-1)+1)*m**6 # _Chai Wah Wu_, Aug 20 2024
%Y Cf. A000961, A037253.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Dec 28 2022