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A359129
q^12*(q^8+q^4+1)*(q^6-1)*(q^2-1) as q runs through the prime powers A000961.
1
0, 211341312, 20560831566912, 67802350642790400, 35817806390625000000, 450782974156649555296512, 19045158721552047314829312, 516964372056378442547769600, 143027806714329275383382337600, 15411735887347424297802263464512
OFFSET
1,2
COMMENTS
For n>1, the order of the twisted Chevalley group (3)D_4(q).
REFERENCES
R. W. Carter, Simple Groups of Lie Type, Wiley 1972, Chap. 14, p. 262.
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.
PROG
(Python)
from sympy import primepi, integer_nthroot
def A359129(n):
def f(x): return int(n-2+x-sum(primepi(integer_nthroot(x, k)[0]) for k in range(1, x.bit_length())))
kmin, kmax = 1, 2
while f(kmax) >= kmax:
kmax <<= 1
while True:
kmid = kmax+kmin>>1
if f(kmid) < kmid:
kmax = kmid
else:
kmin = kmid
if kmax-kmin <= 1:
break
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
CROSSREFS
Sequence in context: A105294 A288079 A037253 * A064588 A202572 A198169
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 28 2022
STATUS
approved