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A134888 E_8 numbers: a(n) = 2^(2*n) * 3^(3*n) * 5^n * 839^n. (Constants are prime numbers). 5

%I

%S 1,453060,205263363600,92996619512616000,42133048436385804960000,

%T 19088798924588952795177600000,8648371240774270953383163456000000,

%U 3918231074345191198139776035375360000000,1775193770542832324229206930587160601600000000

%N E_8 numbers: a(n) = 2^(2*n) * 3^(3*n) * 5^n * 839^n. (Constants are prime numbers).

%C The result of the exceptional Lie group E_8 calculation is a matrix with 453060 rows and columns. Size of the matrix.. = a(1) = 453060. Number of entries... = a(2) = 205263363600.

%H Andrew Howroyd, <a href="/A134888/b134888.txt">Table of n, a(n) for n = 0..100</a>

%H The American Institute of Mathematics, <a href="http://aimath.org/E8">Mathematicians Maps E_8</a>.

%F a(n) = 2^(2*n) * 3^(3*n) * 5^n * 839^n.

%F O.g.f.: 1/(1-453060*x). - _R. J. Mathar_, Nov 24 2007

%F a(n) = 453060^n.

%e a(1) = 453060 because 2^(2*1)=4, 3^(3*1)=27, 5^1=5, 839^1=839 and we can write 4*27*5*839 = 453060.

%e a(2) = 205263363600 because 2^(2*2)=16, 3^(3*2)=729, 5^2=25, 839^2=703921 and we can write 16*729*25*703921=205263363600.

%e a(1)^2 = a(2): 453060*453060 = 205263363600.

%Y Cf. A064730, A134950, A134960, A135639.

%K nonn

%O 0,2

%A _Omar E. Pol_, Nov 22 2007

%E Terms a(5) and beyond from _Andrew Howroyd_, Feb 02 2020

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Last modified January 17 23:09 EST 2021. Contains 340249 sequences. (Running on oeis4.)