A000001 -id:A000001 - cp's OEIS frontend

A055561 Numbers m such that there are precisely 3 groups of order m.

75, 363, 609, 867, 1183, 1265, 1275, 1491, 1587, 1725, 1805, 2067, 2175, 2373, 2523, 3045, 3525, 3685, 3795, 3975, 4137, 4205, 4335, 4425, 4895, 5019, 5043, 5109, 5901, 5915, 6171, 6225, 6627, 6675, 6699, 7935, 8025, 8427, 8475, 8855, 9429, 9537, 10275

Offset: 1

Christian G. Bower, May 25 2000; Nov 12 2003; Feb 17 2006

nonn

Let gnu(n) (= A000001(n)) denote the "group number of n" defined in A000001 or in (J. H. Conway, Heiko Dietrich and E. A. O'Brien, 2008), then the sequence n -> gnu(a(n)) -> gnu(gnu(a(n))) consists of 1's. - Muniru A Asiru, Nov 19 2017
From Jianing Song, Dec 05 2021: (Start)
Contains all numbers of the form k = p*q^2, where p, q are odd primes such that q == -1 (mod p) (see A350245). The 3 groups are C_(p*q^2), C_q X C_(p*q) and (C_q X C_q) : C_p, where : means semidirect product. The third group, which is the only non-abelian group of order k, can be constructed as follows: in F_q the polynomial x^(p-1) + x^(p-2) + ... + x + 1 factors into quadratic polynomials. Pick one factor x^2 + a*x + b (all factors give the same group), then (C_q X C_q) : C_p has representation .
It seems that all terms are odd. (End)

			For m = 75, the 3 groups of order 75 are C75, (C5 x C5) : C3, C15 x C5 and for m = 363 the 3 groups of order 363 are C363, (C11 x C11) : C3, C33 x C11 where C is the Cyclic group of the stated order. The symbols x and : mean direct and semi-direct products respectively. - _Muniru A Asiru_, Oct 24 2017

Gheorghe Coserea, Table of n, a(n) for n = 1..234567, terms 1..206 from Muniru A Asiru.
H. U. Besche, B. Eick and E. A. O'Brien, The Small Groups Library
H. U. Besche, B. Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.
J. H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica, Math. Intell., Vol. 30, No. 2, Spring 2008.
Gordon Royle, Numbers of Small Groups [dead link]
Index entries for sequences related to groups

Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), this sequence (k=3), A054396 (k=4), A054397 (k=5), A135850 (k=6), A249550 (k=7), A249551 (k=8), A249552 (k=9), A249553 (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A350245 is a subsequence.

is(n) = {
  my(p = gcd(n, eulerphi(n)),f,g);
  if (isprime(p), return(n % p^2 == 0 && isprime(gcd(p+1, n))));
  if (omega(p) != 2 || !issquarefree(n), return(0));
  f = factor(n); g = factor(p);
  1 == g[2,1] % g[1,1] &&
  1 == sum(k=1, matsize(f)[1], f[k,1] % g[1,1] == 1) &&
  1 == sum(k=1, matsize(f)[1], f[k,1] % g[2,1] == 1);
};
seq(N) = {
  my(a = vector(N), k=0, n=1);
  while(k < N, if(is(n), a[k++]=n); n++); a;
};
seq(43) \\ Gheorghe Coserea, Dec 12 2017

A001034 Orders of noncyclic simple groups (without repetition).

Original entry on oeis.org

60, 168, 360, 504, 660, 1092, 2448, 2520, 3420, 4080, 5616, 6048, 6072, 7800, 7920, 9828, 12180, 14880, 20160, 25308, 25920, 29120, 32736, 34440, 39732, 51888, 58800, 62400, 74412, 95040, 102660, 113460, 126000, 150348, 175560, 178920

Offset: 1

N. J. A. Sloane, Simon Plouffe

An alternative definition, to assist in searching: Orders of non-cyclic finite simple groups.
This comment is about the three sequences A001034, A060793, A056866: The Feit-Thompson theorem says that a finite group with odd order is solvable, hence all numbers in this sequence are even. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 08 2001 [Corrected by Isaac Saffold, Aug 09 2021]
The primitive elements are A257146. These are also the primitive elements of A056866. - Charles R Greathouse IV, Jan 19 2017
Conjecture: This is a subsequence of A083207 (Zumkeller numbers). Verified for n <= 156. A fast provisional test was used, based on Proposition 17 from Rao/Peng JNT paper (see A083207). For those few cases where the fast test failed (such as 2588772 and 11332452) the comprehensive (but much slower) test by T. D. Noe at A083207 was used for result confirmation. - Ivan N. Ianakiev, Jan 11 2020
From M. Farrokhi D. G., Aug 11 2020: (Start)
The conjecture is not true. The smallest and the only counterexample among the first 457 terms of the sequence is a(175) = 138297600.
On the other hand, the orders of sporadic simple groups are Zumkeller. And with the exception of the smallest two orders 7920 and 95040, the odd part of the other orders are also Zumkeller. (End)
Every term in this sequence is divisible by 4*p*q, where p and q are distinct odd primes. - Isaac Saffold, Oct 24 2021

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].
Dickson L.E. Linear groups, with an exposition of the Galois field theory (Teubner, 1901), p. 309.
M. Hall, Jr., A search for simple groups of order less than one million, pp. 137-168 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

M. Farrokhi D. G., Table of n, a(n) for n = 1..10000
C. Cato, The orders of the known simple groups as far as one trillion, Math. Comp., 31 (1977), 574-577.
L. E. Dickson, Linear Groups with an Exposition of the Galois Field Theory (page images), Dover, NY, 1958, p. 309.
M. Farrokhi D. G., A GAP function generating the smallest non-cyclic finite simple group order greater than a given number m.
Walter Feit and J. G. Thompson, A solvability criterion for finite groups and some consequences, Proc. N. A. S. 48 (6) (1962) 968.
M. Hall Jr., Simple groups of order less than one million, J. Alg. 20 (1) (1972) 98-102
David A. Madore, More terms
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 5.
Index entries for sequences related to groups
Index entries for "core" sequences

Cf. A000001, A000679, A005180, A001228, A060793, A056866, A056868, A119630.

Cf. A109379 (orders with repetition), A119648 (orders that are repeated).

A054396 Numbers m such that there are precisely 4 groups of order m.

Original entry on oeis.org

28, 30, 44, 63, 66, 70, 76, 92, 102, 117, 124, 130, 138, 154, 170, 172, 174, 182, 188, 190, 230, 236, 238, 246, 266, 268, 275, 279, 282, 284, 286, 290, 315, 316, 318, 322, 332, 354, 370, 374, 387, 412, 418, 426, 428, 430, 434, 442, 465, 470, 494, 495, 498

Offset: 1

N. J. A. Sloane, May 21 2000

nonn

			For m = 28, the 4 groups of order 8 are C7 : C4, C28, D28, C14 x C2 and for m = 30 the 4 groups of order 30 are C5 x S3, C3 x D10, D30, C30 where C, D mean cyclic, dihedral groups of the stated order and S is the symmetric group of the stated degree. The symbols x and : mean direct and semidirect products respectively. - _Muniru A Asiru_, Nov 04 2017

Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..10000 (terms 1..369 from Muniru A Asiru).
H. U. Besche, B. Eick and E. A. O'Brien, The Small Groups Library
Gordon Royle, Numbers of Small Groups
Index entries for sequences related to groups

Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), this sequence (k=4), A054397 (k=5), A135850 (k=6), A249550 (k=7), A249551 (k=8), A249552 (k=9), A249553 (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A054396 := Filtered([1..2015], n -> NumberSmallGroups(n) = 4); # Muniru A Asiru, Nov 04 2017

Select[Range[500], FiniteGroupCount[#] == 4 &] (* Jean-François Alcover, Dec 08 2017 *)

Sequence is { m | A000001(m) = 4 }. - Muniru A Asiru, Nov 04 2017

More terms from Christian G. Bower, May 25 2000

A000679 Number of groups of order 2^n.

Original entry on oeis.org

1, 1, 2, 5, 14, 51, 267, 2328, 56092, 10494213, 49487367289

Offset: 0

N. J. A. Sloane

			G.f. = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 51*x^5 + 267*x^6 + 2328*x^7 + ...

James Gleick, Faster, Vintage Books, NY, 2000 (see pp. 259-261).
M. Hall, Jr. and J. K. Senior, The Groups of Order 2^n (n <= 6). Macmillan, NY, 1964.
M. F. Newman, Groups of prime-power order (1990). In Groups—Canberra 1989 (pp. 49-62). Springer, Berlin, Heidelberg. See Table 1.
M. F. Newman and E. A. O'Brien, A CAYLEY library for the groups of order dividing 128, Group theory (Singapore, 1987), 437-442, de Gruyter, Berlin-New York, 1989.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. Applebaum, J. Clikeman, J. A. Davis, J. F. Dillon, J. Jedwab, T. Rabbani, K. Smith, and W. Yolland, Constructions of difference sets in nonabelian 2-groups, Alg. Num. Theor. (2023) Vol. 17, No. 2. 359-396. See p. 396.
Hans Ulrich Besche and Bettina Eick, Construction of finite groups, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 387-404.
Hans Ulrich Besche and Bettina Eick, The groups of order at most 1000 except 512 and 768, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 405-413.
Hans Ulrich Besche, Bettina Eick and E. A. O'Brien, The groups of order at most 2000, Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 1-4.
David Burrell, On the number of groups of order 1024, Communications in Algebra, 2021, 1-3.
Hans Ulrich Besche, The Small Groups library
Bettina Eick and E. A. O'Brien, Enumerating p-groups. Group theory. J. Austral. Math. Soc. Ser. A 67 (1999), no. 2, 191-205.
Richard K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
Rodney James and John Cannon, Computation of isomorphism classes of p-groups, Mathematics of Computation 23.105 (1969): 135-140.
Rodney James, M. F. Newman, and E. A. O'Brien, The Groups of Order 128, J. Algebra 129, 136-158, 1990.
G. A. Miller, Determination of all the groups of order 64, Amer. J. Math., 52 (1930), 617-634.
E. A. O'Brien, The Groups of Order 256 J. Algebra 143, 219-235, 1991.
Eugene Rodemich, The groups of order 128, J. Algebra 67 (1980), no. 1, 129-142.
Eric Weisstein's World of Mathematics, Finite Group.
Marcel Wild, The groups of order 16 made easy, Amer. Math. Monthly, 112 (No. 1, 2005), 20-31.
Index entries for sequences related to groups.

Cf. A000001, A046058.

A000679 := List([0..8],n -> NumberSmallGroups(2^n)); # Muniru A Asiru, Oct 15 2017

seq(GroupTheory:--NumGroups(2^n),n=0..10); # Robert Israel, Oct 15 2017

Join[{1}, FiniteGroupCount[2^Range[10]]] (* Vincenzo Librandi, Mar 28 2018 *)

a(n) = 2^((2/27)n^3 + O(n^(8/3))).

a(n) = A000001(2^n). - Amiram Eldar, Mar 10 2024

a(9) and a(10) found by Eamonn O'Brien

a(10) corrected by David Burrell, Jun 06 2022

A031214 Initial term of sequence An.

Original entry on oeis.org

0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 2, 2, 1, 2, 1, 1, 2, 1, 0, 1, 1, 1, 0, 1, 2, 8, 14, 4, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 0, 4, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1

Offset: 1

Jeff Burch

This ignores the offset and gives the first term of the actual entry.
Since the sequences in the OEIS occasionally change their initial terms (for editorial reasons), this is an especially ill-defined sequence! - N. J. A. Sloane, Jan 01 2005
Sequences like this are deprecated. - Joerg Arndt, Apr 16 2020

			A000001 begins 0,1,1,1,2,1,2,1,5,2,... so a(1) = 0 = a(31214).

PrimeFan, Esoteric Integer Sequences
PrimeFan, Esoteric Integer Sequences [Cached copy]
N. J. A. Sloane, Online Encyclopedia of Integer Sequences
Index entries for sequences whose definition involves A_n (or An).

Cf. A039928, A051070, A091967, A107357, A102288; also A000001, A000002, A000003, A000004, A000005, etc.

Data updated by Sean A. Irvine, Apr 16 2020

A135850 Numbers m such that there are precisely 6 groups of order m.

Original entry on oeis.org

42, 78, 110, 114, 147, 186, 222, 225, 258, 310, 366, 402, 406, 410, 438, 474, 506, 507, 525, 582, 602, 610, 618, 654, 710, 735, 762, 834, 906, 942, 975, 978, 994, 1010, 1083, 1086, 1089, 1158, 1194, 1266, 1310, 1338, 1374, 1378, 1425, 1446, 1474, 1510, 1582

Offset: 1

N. J. A. Sloane, based on a suggestion from Neven Juric, Mar 08 2008

nonn

Let gnu(n) = A000001(n) denote the "group number of n" defined in A000001 or in (J. H. Conway, Heiko Dietrich and E. A. O'Brien, 2008), then the sequence n -> gnu(a(n)) -> gnu(gnu(a(n))) -> gnu(gnu(gnu(a(n)))) consists of 1's. - Muniru A Asiru, Nov 19 2017

			For m = 42, the 6 groups of order 42 are (C7 : C3) : C2, C2 x (C7 : C3), C7 x S3, C3 x D14, D42, C42 and for n = 78 the 6 groups of order 78 are (C13 : C3) : C2, C2 x (C13 : C3), C13 x S3, C3 x D26, D78, C78 where C, D mean Cyclic, Dihedral groups of the stated order and S is the Symmetric group of the stated degree. The symbols x and : mean direct and semidirect products respectively. - _Muniru A Asiru_, Nov 04 2017

Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..1099 (terms 1..91 from Muniru A Asiru).
J. H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica, Math. Intell., Vol. 30, No. 2, Spring 2008.
Index entries for sequences related to groups

Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), A054396 (k=4), A054397 (k=5), this sequence (k=6), A249550 (k=7), A249551 (k=8), A249552 (k=9), A249553 (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A135850 := Filtered([1..2015], n -> NumberSmallGroups(n) = 6); # Muniru A Asiru, Nov 04 2017

Select[Range[10^4], FiniteGroupCount[#] == 6 &] (* Robert Price, May 23 2019 *)

Sequence is { m | A000001(m) = 6 }. - Muniru A Asiru, Nov 04 2017

A249551 Numbers m such that there are precisely 8 groups of order m.

Original entry on oeis.org

510, 690, 870, 910, 1122, 1190, 1330, 1395, 1410, 1590, 1610, 1770, 1914, 2002, 2210, 2346, 2470, 2490, 2590, 2618, 2670, 2706, 2745, 2926, 2958, 2990, 3094, 3102, 3210, 3230, 3290, 3390, 3458, 3465, 3498, 3710, 3770, 3894, 3910, 4002, 4110, 4130, 4182, 4186, 4370, 4470

Offset: 1

N. J. A. Sloane, Nov 01 2014

nonn

Muniru A Asiru, Table of n, a(n) for n = 1..1064
H. U. Besche, B. Eick and E. A. O'Brien, Numbers of isomorphism types of finite groups of given order
Index entries for sequences related to groups

Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), A054396 (k=4), A054397 (k=5), A135850 (k=6), A249550 (k=7), this sequence (k=8), A249552 (k=9), A249553 (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A249551 := Filtered([1..2015], n -> NumberSmallGroups(n) = 8); # Muniru A Asiru, Oct 18 2017

Select[Range[10^4], FiniteGroupCount[#] == 8 &] (* A current limit in Mathematica is such that some orders >2047 may not be evaluated.*) (* Robert Price, May 24 2019 *)

a(15)-a(16) from Muniru A Asiru, Oct 18 2017
More terms from Michael De Vlieger, Oct 18 2017
Missing terms added by Andrey Zabolotskiy, Oct 27 2017

A249552 Numbers m such that there are precisely 9 groups of order m.

Original entry on oeis.org

308, 532, 644, 836, 868, 1316, 1364, 1652, 1748, 1815, 1876, 1892, 2068, 2212, 2324, 2356, 2596, 2852, 2884, 2996, 3124, 3268, 3476, 3572, 3652, 3668, 3892, 3956, 4228, 4263, 4484, 4532, 4564, 4676, 4708, 5012, 5092, 5332, 5348, 5396, 5428, 5572, 5588, 5764, 5828, 6004, 6116, 6164, 6244, 6308, 6356, 6532

Offset: 1

N. J. A. Sloane, Nov 01 2014

nonn

Muniru A Asiru and Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..456
Max Horn, Numbers of isomorphism types of finite groups of given order
Index entries for sequences related to groups

Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), A054396 (k=4), A054397 (k=5), A135850 (k=6), A249550 (k=7), A249551 (k=8), this sequence (k=9), A249553 (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A249552:=Filtered([1..2015],n->NumberSmallGroups(n)=9); # Muniru A Asiru, Nov 17 2017

select(t -> GroupTheory:-NumAbelianGroups(t) <= 9 and GroupTheory:-NumGroups(t) = 9, [$1..10000]); # Robert Israel, Mar 26 2018

a(13)-a(16) from Muniru A Asiru, Oct 21 2017
More terms from Muniru A Asiru, Oct 23 2017
More terms from Muniru A Asiru, Nov 17 2017
Incorrect b-file shortened by Jorge R. F. F. Lopes, Jan 07 2022

A249553 Numbers m such that there are precisely 10 groups of order m.

Original entry on oeis.org

90, 132, 198, 276, 306, 350, 414, 490, 522, 564, 650, 708, 738, 846, 850, 852, 950, 954, 996, 1062, 1078, 1150, 1274, 1278, 1284, 1450, 1485, 1494, 1572, 1602, 1666, 1690, 1694, 1818, 1850, 1862, 1926, 2004, 2034, 2148, 2150, 2254, 2292, 2325, 2350, 2358, 2466, 2475, 2650, 2682, 2724, 2868, 2890, 2950, 3006, 3012, 3038, 3114, 3146, 3156

Offset: 1

N. J. A. Sloane, Nov 01 2014

nonn

Muniru A Asiru, Table of n, a(n) for n = 1..799
Index entries for sequences related to groups

Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), A054396 (k=4), A054397 (k=5), A135850 (k=6), A249550 (k=7), A249551 (k=8), A249552 (k=9), this sequence (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A249553 := Filtered([1..2015], n -> NumberSmallGroups(n) = 10); # Muniru A Asiru, Oct 16 2017

Select[ Range@2047, FiniteGroupCount@# == 10 &] (* Robert G. Wilson v, Nov 30 2017 *)

More terms from Michael De Vlieger, Oct 16 2017

More terms from Muniru A Asiru, Oct 24 2017

A249554 Numbers m such that there are precisely 11 groups of order m.

Original entry on oeis.org

140, 364, 380, 460, 476, 572, 748, 819, 860, 940, 988, 1036, 1148, 1180, 1196, 1276, 1292, 1340, 1484, 1564, 1580, 1612, 1628, 1660, 1708, 1804, 1953, 2044, 2060, 2108, 2140, 2204, 2236, 2332, 2444, 2492, 2540, 2668, 2684, 2716, 2780, 2812, 2828, 2924, 3052, 3068, 3116, 3196, 3212

Offset: 1

N. J. A. Sloane, Nov 01 2014

nonn

Muniru A Asiru, Table of n, a(n) for n = 1..929
Index entries for sequences related to groups

Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), A054396 (k=4), A054397 (k=5), A135850 (k=6), A249550 (k=7), A249551 (k=8), A249552 (k=9), A249553 (k=10), this sequence (k=11), A249555 (k=12), A292896 (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A249554 := Filtered([1..2015], n -> NumberSmallGroups(n) = 11); # Muniru A Asiru, Oct 16 2017

with(GroupTheory): select(n->NumGroups(n)=11,[$1..4000]); # Muniru A Asiru, Mar 28 2018

Select[Range[10^4], FiniteGroupCount[#] == 11 &] (* A current limit in Mathematica is such that some orders >2047 may not be evaluated.*)(* Robert Price, May 24 2019 *)

More terms added by Muniru A Asiru, Oct 23 2017

Incorrect b-file shortened by Andrew Howroyd, Jan 28 2022

cp's OEIS Frontend

A055561 Numbers m such that there are precisely 3 groups of order m.

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A001034 Orders of noncyclic simple groups (without repetition).

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A054396 Numbers m such that there are precisely 4 groups of order m.

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A000679 Number of groups of order 2^n.

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A031214 Initial term of sequence An.

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A135850 Numbers m such that there are precisely 6 groups of order m.

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A249551 Numbers m such that there are precisely 8 groups of order m.

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A249552 Numbers m such that there are precisely 9 groups of order m.

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