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 1-9 of 9 results.

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

Views

Author

N. J. A. Sloane

Keywords

Examples

			808017424794512875886459904961710757005754368000000000.

References

  • 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.

Crossrefs

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

Programs

  • PARI
    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

Formula

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

A174601 Numbers of divisors of orders of sporadic simple groups.

Original entry on oeis.org

60, 112, 128, 192, 192, 384, 480, 384, 704, 896, 1056, 1920, 2688, 3200, 2816, 4256, 4320, 5880, 16128, 16896, 25536, 26400, 45056, 143616, 1580544, 424488960
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 02 2010

Keywords

Comments

a(n) = A000005(A001228(n)).

Examples

			a(1) = A000005(7920) = A000005(2^4 * 3^2 * 5^1 * 11^1) = (4+1)*(2+1)*(1+1)*(1+1) = 60;
a(26) = PROD((A051161(k)+1): k>0) = (46+1)*(20+1)*(9+1)*(6+1)*(2+1)*(3+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(0+1)*(1+1)*(0+1)*(1+1)*(0+1)*(1+1)*(0+1)*(0+1)*(1+1)*(0+1)*(0+1)*... = 47*21*10*7*3*4*2*2*2*2*2*1*2*1*2*1*2*1*1*2*1*1*... = 424488960.

Links

Crossrefs

Cf. A174670.

A174671 Divisors of the order of the Monster group, sorted into decreasing order.

Original entry on oeis.org

808017424794512875886459904961710757005754368000000000, 404008712397256437943229952480855378502877184000000000, 269339141598170958628819968320570252335251456000000000, 202004356198628218971614976240427689251438592000000000, 161603484958902575177291980992342151401150873600000000
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 02 2010

Keywords

Comments

Let Mnr = A001228(26) = 808017424794512875886459904961710757005754368000000000, also called the Monster number, cf. A003131;
a(n) = Mnr / A174670(n);
the sequence is finite with A174601(26) = 424488960 terms;
a(n) = A174670(424488960 - n + 1).

Examples

			a(1) = Mnr;
a(424488960) = 1, the last term.

Links

A174848 Squarefree kernels of orders of sporadic simple groups.

Original entry on oeis.org

330, 330, 43890, 2310, 210, 53130, 2310, 9690, 53130, 2310, 3570, 79170, 30030, 1360590, 53130, 53130, 30030, 43890, 177521190, 1607970, 11741730, 690690, 75992317170, 340510170, 325046311590, 1618964990108856390
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 02 2010

Keywords

Comments

a(n) = A007947(A001228(n)).

Examples

			a(1) = 2*3*5*11;
a(2) = 2*3*5*11;
a(3) = 2*3*5*7*11*19;
a(4) = 2*3*5*7*11 = 11#;
a(5) = 2*3*5*7 = 7#;
a(6) = 2*3*5*7*11*23;
a(7) = 2*3*5*7*11 = 11#;
a(8) = 2*3*5*17*19;
a(9) = 2*3*5*7*11*23;
a(10) = 2*3*5*7*11 = 11#;
a(11) = 2*3*5*7*17;
a(12) = 2*3*5*7*13*29;
a(13) = 2*3*5*7*11*13 = 13#;
a(14) = 2*3*5*7*11*19*31;
a(15) = 2*3*5*7*11*23;
a(16) = 2*3*5*7*11*23;
a(17) = 2*3*5*7*11*13 = 13#;
a(18) = 2*3*5*7*11*19;
a(19) = 2*3*5*7*11*31*37*67;
a(20) = 2*3*5*7*13*19*31;
a(21) = 2*3*5*7*11*13*17*23;
a(22) = 2*3*5*7*11*13*23;
a(23) = 2*3*5*7*11*23*29*31*37*43;
a(24) = 2*3*5*7*11*13*17*23*29;
a(25) = 2*3*5*7*11*13*17*19*23*31*47;
a(26) = PROD(A002267(k): 1<=k<=15) = 2*3*5*7*11*13*17*19*23*29*31*41*47*59*71.

Links

Crossrefs

Cf. A174670.

A174818 a(n) = A174817(n) - Mnr; where Mnr = A001228(26) = 808017424794512875886459904961710757005754368000000000, also called the Monster number, cf. A003131.

Original entry on oeis.org

-43, -53, 83, -197, 283, -313, 431, -433, -439, -673, -733, 823, 881, 997, 1061, -1093, -1123, 1223, 1303, 1307, 1327, 1381, -1451, 1453, -1471, -1531, 1549, 1583, -1607, -1667, 1709, 1721, -1787, 1787, 1949, -1973, 1993, 2039, 2083, -2099, 2129
Offset: 1

Views

Author

Reinhard Zumkeller, Apr 02 2010

Keywords

Comments

The absolute values of the terms are non-divisors of Mnr (complement of A174670); the smallest composite term is ABS(a(43))=2479=37*67.

Links

Crossrefs

Cf. A003131, A001228, A174670, A174817.

A212554 Products of supersingular primes (A002267).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 75, 76, 77, 78, 80, 81, 82, 84, 85, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100
Offset: 1

Views

Author

Ben Branman, May 21 2012

Keywords

Comments

The initial 1 is included because it has no non-supersingular prime factors.
Many of the early terms divide the order of the monster simple group (see A174670). The first n such that a(n) does not belong to A174670 is a(204)=289.

References

  • 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].
  • J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
  • 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.

Links

Crossrefs

Cf. A002267, A174670, A108764 (products of exactly two supersingular primes).

Programs

  • Mathematica
    ps = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71}; fQ[n_] := Module[{p = Transpose[FactorInteger[n]][[1]]}, Complement[p, ps] == {}]; Join[{1}, Select[Range[2,1000], fQ]] (* T. D. Noe, May 21 2012 *)

Formula

log a(n) ~ k*n^(1/15). - Charles R Greathouse IV, Jul 18 2012

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

Views

Author

Omar E. Pol, Nov 03 2011

Keywords

Comments

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).

Links

Crossrefs

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

Programs

A367141 The orders, without repetition, of elements of the Monster simple group.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 54, 55, 56, 57, 59, 60, 62, 66, 68, 69, 70, 71, 78, 84, 87, 88, 92, 93, 94, 95, 104, 105, 110, 119
Offset: 1

Views

Author

Hal M. Switkay, Nov 06 2023

Keywords

Comments

There are 194 conjugacy classes of elements in the Monster. There are 10 conjugacy classes of elements of orders 12 and 24 each, more than for any other order.
a(n) = n for n <= 36. 37 is the smallest natural number not to divide the order of the Monster.

References

  • 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].

Links

Crossrefs

Cf. A174670, A366481.

A329191 The prime divisors of the orders of the sporadic finite simple groups.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 59, 67, 71
Offset: 1

Views

Author

Hal M. Switkay, Nov 07 2019

Keywords

Comments

This list is complete according to the classification theorem for finite simple groups.
This list includes all primes < 72 except 53 and 61, which do not divide the order of any sporadic finite simple group.
All entries on this list divide the order of the Monster, except 37, 43, and 67.

Examples

			The first term is necessarily 2, by the Feit-Thompson theorem.

References

  • 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].

Links

  • R. A. Wilson et al., ATLAS of Finite Group Representations, version 3, Sporadic groups

Crossrefs

Cf. A001228, A005180, A174670.
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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