A134950 -id:A134950 - 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)

A134960 a(n) = n*453060.

Original entry on oeis.org

0, 453060, 906120, 1359180, 1812240, 2265300, 2718360, 3171420, 3624480, 4077540, 4530600, 4983660, 5436720, 5889780, 6342840, 6795900, 7248960, 7702020, 8155080, 8608140, 9061200, 9514260, 9967320, 10420380, 10873440, 11326500, 11779560, 12232620, 12685680, 13138740

Offset: 0

Omar E. Pol, Nov 27 2007

The first positive member of this sequence and some of its multiples are related to the exceptional Lie group E_8 calculation. The result of the calculation is a matrix with 453060 rows and columns. The size of the matrix is a(1)=453060 and the number of entries of the matrix is a(453060)=453060*453060=205263363600.

			a(1) = 453060. a(453060) = 453060*453060 = 205263363600.

The American Institute of Mathematics, Mathematicians Maps E_8.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A064730, A134888, A134950, A135639.

453060 Range[0,30] (* Harvey P. Dale, Oct 11 2023 *)

concat(0, Vec(453060*x/(x-1)^2 + O(x^30))) \\ Elmo R. Oliveira, Jul 05 2025

From Elmo R. Oliveira, Jul 05 2025: (Start)
G.f.: 453060*x/(1-x)^2.
E.g.f.: 453060*x*exp(x).
a(n) = 540*A135639(n).
a(n) = 2*a(n-1) - a(n-2). (End)

More terms from Elmo R. Oliveira, Jul 05 2025

A018509 Divisors of 540.

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

Offset: 1

N. J. A. Sloane

Index entries for sequences related to divisors of numbers

Cf. A134950.

Divisors[540] (* Harvey P. Dale, Aug 27 2017 *)

divisors(540) \\ Charles R Greathouse IV, Jun 21 2017

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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A134960 a(n) = n*453060.

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A018509 Divisors of 540.

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PARI

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