A001379 -id:A001379 - cp's OEIS frontend

A244431 Indices of repeated terms in A001379, the list of degrees of irreducible representations of Monster group M.

16, 17, 26, 27, 39, 40, 41, 42, 44, 45, 47, 48, 53, 54, 55, 56, 59, 60, 71, 72, 74, 75, 81, 82, 83, 84, 85, 86, 89, 90, 99, 100, 102, 103, 105, 106, 107, 108, 123, 124, 125, 128, 129, 135, 136, 179, 180

Offset: 1

Omar E. Pol, Nov 28 2014

A001379 has 194 terms, but the number of distinct terms is 194 - 23 - 1 = 194 - 24 = 170.

			The only triple in A001379 is A001379(123) = A001379(124) = A001379(125) = 5514132424881463208443904. The rest of the repeated terms are pairs, for example; the first of them is A001379(16) = A001379(17) = 8980616927734375, so a(1) = 16 and a(2) = 17.

Eric Weisstein's World of Mathematics, Monstrous Moonshine

Cf. A001379, A247156.

A247156 Numbers that are repeated in A001379.

Original entry on oeis.org

8980616927734375, 3503434660075044981, 172399434201593354756, 286243267692724486144, 640558364167263622626, 691170144025469730622, 1480279477146615234375, 1768130802583126953125, 4567199176912486400000, 42940402913709544921875, 70660346341309333984375, 149614794149226010902528, 161649111002260792968750, 191259085113459945312500, 260799524107083767968750, 597787522207315571077947, 626877403613887304040448, 689763222744895005949242, 689766726179555080994223, 5514132424881463208443904, 7567151576542452425781250, 9592298143650890255171584, 136574874874360806036041889

Offset: 1

Omar E. Pol, Nov 28 2014

Apart of the single numbers, A001379 contains two copies of every term of this sequence, except of a(20) = 5514132424881463208443904 which A001379 contains three copies.

Eric Weisstein's World of Mathematics, Monstrous Moonshine

Cf. A001379, A244431.

A278566 Irregular triangle read by rows: row n gives coefficients when the n-th coefficient of the modular function j (A000521(n)) is written as a linear combination of irreducible characters of the Monster simple group (A001379).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 3, 1, 2, 1, 4, 5, 3, 2, 1, 1, 1

Offset: 1

N. J. A. Sloane, Nov 26 2016

The coefficients are given as in Thompson's paper. The choice of coefficients is actually ambiguous because of a linear relation with small coefficients between the terms of A001379 (see Wikipedia). - Andrey Zabolotskiy, Feb 12 2019

			Triangle begins:
  1,1,
  1,1,1,
  2,2,1,1,
  3,3,1,2,1,
  4,5,3,2,1,1,1,
  ...

J. G. Thompson, Some numerology between the Fischer-Griess Monster and the elliptic modular function, Bull. London Math. Soc., 11 (1979), 352-353.
Wikipedia, Monstrous moonshine
Index entries for sequences related to groups
Index entries for McKay-Thompson series for Monster simple group

Cf. A000521, A001379, A007240, A055791.

A002267 The 15 supersingular primes: primes dividing order of Monster simple group.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71

Offset: 1

N. J. A. Sloane

The supersingular primes are a subset of the Chen primes (A109611). - Paul Muljadi, Oct 12 2005

PROD(a(k): 1<=k<=15) = 1618964990108856390 = A174848(26). - Reinhard Zumkeller, Apr 02 2010

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].
A. P. Ogg, Modular functions, in The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), pp. 521-532, Proc. Sympos. Pure Math., 37, Amer. Math. Soc., Providence, R.I., 1980.

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
T. Gannon, Postcards from the edge, or Snapshots of the theory of generalised Moonshine, arXiv:math/0109067 [math.QA], 2001.
Alan W. Reid, Arithmetic hyperbolic manifolds, slides of a talk, Cornell University, June 2014,
G. K. Sankaran, A supersingular coincidence, arXiv:2009.11379 [math.NT], 2020.
J. G. Thompson, Finite groups and modular functions, Bulletin of the London Mathematical Society 11.3 (1979): 347-351. See page 350.
Eric Weisstein's World of Mathematics, Supersingular Prime
Index entries for sequences related to groups

Cf. A003131, A001379, A051161, A109611.

FactorInteger[GroupOrder[MonsterGroupM[]]][[All, 1]] (* Jean-François Alcover, Oct 03 2016 *)

A002267=vecextract(primes(20),612351) \\ bitmask 2^20-1-213<<11: remove primes # 12, 14, 16, 18 and 19. - M. F. Hasler, Nov 10 2017

A003131 Order of Monster simple group.

Original entry on oeis.org

8, 0, 8, 0, 1, 7, 4, 2, 4, 7, 9, 4, 5, 1, 2, 8, 7, 5, 8, 8, 6, 4, 5, 9, 9, 0, 4, 9, 6, 1, 7, 1, 0, 7, 5, 7, 0, 0, 5, 7, 5, 4, 3, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 54

N. J. A. Sloane

			808017424794512875886459904961710757005754368000000000.

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. 228.
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 296.
J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, New York, 1996, p. 62.
C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 474.

Cf. A001228, A001379, A002267, A051161, A174670, A174817.

2^46 * 3^20 * 5^9 * 7^6 * 11^2 * 13^3 * 17 * 19 * 23 * 29 * 31 * 41 * 47 * 59 * 71 \\ Charles R Greathouse IV, Oct 31 2014

Equals A001228(26) = Product_{n=1..15} A002267(n)^A051161(A049084(A002267(n))) = Sum_{n=0..53} a(53-n)*10^n = h(53) with h(n) = 10*h(n-1) + a(n) for n > 0, h(0) = a(0). - Reinhard Zumkeller, Apr 02 2010

A051161 a(n) is the exponent of n-th prime in the order (A003131) of the Monster simple group.

Original entry on oeis.org

46, 20, 9, 6, 2, 3, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

N. J. A. Sloane

nonn

a(n)=0 for n > 20.

Product_{k>0} (a(k) + 1) = A174601(26). - Reinhard Zumkeller, Apr 02 2010

Cf. A003131, A001379, A002267, A174601.

A199014 Divisors of 196884.

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 1823, 3646, 5469, 7292, 10938, 16407, 21876, 32814, 49221, 65628, 98442, 196884

Offset: 1

Omar E. Pol, Nov 03 2011

196884 =2^2*3^3*1823 is the third coefficient of modular function j (see A000521). 196884 has 24 divisors. Its first 12 divisors are the divisors of 108 =2^2*3^3 (see A018287).

Index entries for sequences related to divisors of numbers

Cf. A000521, A001379, A018253, A018287, A018623, A174670, A174671.

Divisors[196884] (* Harvey P. Dale, Jan 16 2022 *)

divisors(196884) \\ Charles R Greathouse IV, Sep 06 2016

A247235 Divisors of 5844076785304502808013602136.

Original entry on oeis.org

1, 2, 4, 8, 19, 38, 76, 152, 1800829, 3601658, 7203316, 14406632, 34215751, 68431502, 136863004, 273726008, 21350096865126907517, 42700193730253815034, 85400387460507630068, 170800774921015260136, 405651840437411242823, 811303680874822485646, 1622607361749644971292, 3245214723499289942584, 38447873587529623736931593, 76895747175059247473863186, 153791494350118494947726372, 307582988700236989895452744, 730509598163062851001700267, 1461019196326125702003400534, 2922038392652251404006801068, 5844076785304502808013602136

Offset: 1

Omar E. Pol, Nov 27 2014

The integer 5844076785304502808013602136 is the denominator mentioned in the abstract of the Duncan-Griffin-Ono paper. The proportion of 1's in: 1 = 1, 196884 = 1 + 196883, 21493760 = 1 + 196883 + 21296876... tends to 1/5844076785304502808013602136 = 1.7111... * 10^-28.
..
Apparently 5844076785304502808013602136 is the last term of A247242.

John F. R. Duncan, Michael J. Griffin, Ken Ono, Moonshine, arXiv:1411.6571 [math.RT], 2014.
Eric Weisstein's World of Mathematics, j-Function
Eric Weisstein's World of Mathematics, Monstrous Moonshine

Cf. A000521, A001379, A007240, A247242.

Divisors[5844076785304502808013602136] (* Wesley Ivan Hurt, Mar 20 2022 *)

divisors(5844076785304502808013602136) \\ Charles R Greathouse IV, Jun 22 2017

A247242 Partial sums of dimensions of irreducible representations of Monster group M.

Original entry on oeis.org

1, 196884, 21493760, 864103086, 19402853162, 38762915689, 332316649987, 4211531587585, 40384724915584, 165895451930859, 356187797640402, 579067654374651, 1623936121149784, 2733880581665934, 5108005421728910

Offset: 1

Omar E. Pol, Nov 28 2014

Partial sums of A001379.

By definition the sequence contains 194 terms.

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
John F. R. Duncan, Michael J. Griffin, Ken Ono, Moonshine, arXiv:1411.6571 [math.RT]
Eric Weisstein's World of Mathematics, j-Function
Eric Weisstein's World of Mathematics, Monstrous Moonshine

Cf. A000521, A001379, A007240, A247235, A247243.

cp's OEIS Frontend

A244431 Indices of repeated terms in A001379, the list of degrees of irreducible representations of Monster group M.

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A247156 Numbers that are repeated in A001379.

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A278566 Irregular triangle read by rows: row n gives coefficients when the n-th coefficient of the modular function j (A000521(n)) is written as a linear combination of irreducible characters of the Monster simple group (A001379).

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A002267 The 15 supersingular primes: primes dividing order of Monster simple group.

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A003131 Order of Monster simple group.

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A051161 a(n) is the exponent of n-th prime in the order (A003131) of the Monster simple group.

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A199014 Divisors of 196884.

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PARI

A247235 Divisors of 5844076785304502808013602136.

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PARI

A247242 Partial sums of dimensions of irreducible representations of Monster group M.

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