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

1, 453060, 205263363600, 92996619512616000, 42133048436385804960000, 19088798924588952795177600000, 8648371240774270953383163456000000, 3918231074345191198139776035375360000000, 1775193770542832324229206930587160601600000000

Offset: 0

Author

Omar E. Pol, Nov 22 2007

Keywords

• nonn
• easy

Comments

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.

Examples

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100
• The American Institute of Mathematics, Mathematicians Maps E_8.
• Index entries for linear recurrences with constant coefficients, signature (453060).

Crossrefs

Cf. A064730, A134950, A134960, A135639, A135640.

Programs

Mathematica

NestList[453060*# &, 1, 10] (* Paolo Xausa, Jul 14 2025 *)

Formula

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

O.g.f.: 1/(1-453060*x). - R. J. Mathar, Nov 24 2007

a(n) = 453060^n.

From Elmo R. Oliveira, Jul 05 2025: (Start)

E.g.f.: exp(453060*x).

a(n) = 453060*a(n-1).

a(n) = 540^n * A135640(n). (End)

Extensions

Terms a(5) and beyond from Andrew Howroyd, Feb 02 2020