A134960 -id:A134960 - cp's OEIS frontend

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

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

Offset: 0

Omar E. Pol, Nov 22 2007

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.

			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.

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).

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

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

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)

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

A135639 a(n) = 839*n.

Original entry on oeis.org

0, 839, 1678, 2517, 3356, 4195, 5034, 5873, 6712, 7551, 8390, 9229, 10068, 10907, 11746, 12585, 13424, 14263, 15102, 15941, 16780, 17619, 18458, 19297, 20136, 20975, 21814, 22653, 23492, 24331, 25170, 26009, 26848, 27687, 28526

Offset: 0

Omar E. Pol, Nov 27 2007

The 146th prime number (839) and some of its multiples are related to the exceptional Lie group E_8 calculation because the result is a matrix with 453060 rows and columns. The size of the matrix is the member a(540)=453060 of this sequence. The number 839 is the largest prime factor of 453060 because we can write 2*2*3*3*3*5*839=453060. The number of entries of the matrix is the member a(244652400)=453060*453060=205263363600.

			a(1)=839. a(540)=540*839=453060. a(244652400)=244652400*839=205263363600.

G. C. Greubel, Table of n, a(n) for n = 0..1000
American Institute of Mathematics, Mathematicians Maps E_8.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A064730, A134888, A134950, A134960, A135631.

839Range[0,40] (* Harvey P. Dale, Sep 13 2011 *)
LinearRecurrence[{2,-1},{0,839},25] (* G. C. Greubel, Oct 25 2016 *)

From G. C. Greubel, Oct 25 2016: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (839*x)/(1 - x)^2.
E.g.f.: 839*x*exp(x). (End)

A134950 Divisors of 453060.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540, 839, 1678, 2517, 3356, 4195, 5034, 7551, 8390, 10068, 12585, 15102, 16780, 22653, 25170, 30204, 37755, 45306, 50340, 75510, 90612, 113265, 151020, 226530, 453060

Offset: 1

Omar E. Pol, Nov 28 2007

The number 453060 has 48 divisors. Only four are primes: 2, 3, 5 and 839. The sum of divisors is 1411200. The sum of proper divisors is 958140. The number 453060 is related to the exceptional Lie group E_8 calculation. For more information, see A134960.

			453060=540*839.

Index entries for sequences related to divisors of numbers

Cf. A018509, A064730, A134888, A134960, A135639, A135640.

Divisors[453060] (* Harvey P. Dale, Sep 09 2019 *)

divisors(453060) \\ Charles R Greathouse IV, Sep 06 2016

A135640 Powers of 839: a(n) = 839^n.

Original entry on oeis.org

1, 839, 703921, 590589719, 495504774241, 415728505588199, 348796216188498961, 292640025382150628279, 245524981295624377126081, 205995459307028852408781959, 172830190358597207170968063601, 145004529710863056816442205361239, 121658800427414104668995010298079521

Offset: 0

Omar E. Pol, Nov 27 2007

The prime number 839 is related with the exceptional Lie group E_8 calculation. For more information, see: A134888, A134960 and A135639.

			a(2) = 703921 because 839^2 = 839*839 = 703921.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (839).

Cf. A009975, A134888, A134960, A135639.

Table[839^n,{n,0,20}] (* Vincenzo Librandi, Mar 12 2012 *)
NestList[839#&,1,20] (* Harvey P. Dale, Aug 17 2019 *)

a(n) = 839^n.
From Elmo R. Oliveira, Jul 05 2025: (Start)
G.f.: 1/(1-839*x).
E.g.f.: exp(839*x).
a(n) = 839*a(n-1). (End)

cp's OEIS Frontend

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

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A135639 a(n) = 839*n.

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A134950 Divisors of 453060.

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A135640 Powers of 839: a(n) = 839^n.

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