cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

Omar E. Pol, Nov 27 2007

Keywords

Comments

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.

Examples

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

Links

Crossrefs

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

Programs

Formula

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

Views

Author

Omar E. Pol, Nov 28 2007

Keywords

Comments

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.

Examples

			453060=540*839.

Links

Crossrefs

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

Programs

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

Views

Author

Omar E. Pol, Nov 27 2007

Keywords

Comments

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.

Examples

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

Links

Crossrefs

Cf. A064730, A134888, A134950, A135639.

Programs

Formula

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)

Extensions

More terms from Elmo R. Oliveira, Jul 05 2025

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

Views

Author

Omar E. Pol, Nov 27 2007

Keywords

Comments

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

Examples

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

Links

Crossrefs

Cf. A009975, A134888, A134960, A135639.

Programs

Formula

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)
Showing 1-4 of 4 results.

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