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 1-10 of 25 results. Next

A062710 Number of cyclic subgroups of general affine group over GF(2), AGL(n,2).

Original entry on oeis.org

2, 17, 590, 105824, 69300688, 194965719104, 2426497181267968, 177803451495373322240, 52976870608237776911450112, 110350007913361454793759188320256
Offset: 1

Views

Author

Vladeta Jovovic, Jul 13 2001

Keywords

Examples

			a(3) = 1/phi(1)+91/phi(2)+224/phi(3)+420/phi(4)+224/phi(6)+384/phi(7) = 590.
		

References

  • V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.

Crossrefs

Cf. A062250.

Formula

a(n) = Sum_{d} |{g element of AGL(n, 2): order(g)=d}|/phi(d), where phi=Euler totient function, cf. A000010.

A063393 Number of solutions of x^10=1 in general affine group AGL(n,2).

Original entry on oeis.org

2, 10, 92, 23200, 21391520, 35841831040, 95709758320640, 6206883395497062400, 1502803598296957497344000, 654083813715060854940290252800, 450433384822340709737677746549555200
Offset: 1

Views

Author

Vladeta Jovovic, Jul 16 2001

Keywords

Crossrefs

A063385 Number of solutions of x^2=1 in general affine group AGL(n,2).

Original entry on oeis.org

2, 10, 92, 1696, 59552, 4124800, 556101632, 148425895936, 78099471368192, 81705857229783040, 169694608681978560512, 702657511446831375056896, 5797142351555426979908943872, 95500953266115919784543392890880, 3140561514292519005433439594146168832
Offset: 1

Views

Author

Vladeta Jovovic, Jul 16 2001

Keywords

Crossrefs

Extensions

More terms from Sean A. Irvine, Apr 23 2023

A063406 Number of cyclic subgroups of order 3 of general affine group AGL(n,2).

Original entry on oeis.org

0, 4, 112, 3136, 484096, 153545728, 72255188992, 169225143107584, 767806696376172544, 5846826552577416232960, 211692077904149369184059392, 14577670180222125357773973618688
Offset: 1

Views

Author

Vladeta Jovovic, Jul 17 2001

Keywords

Comments

Number of cyclic subgroups of order m in general affine group AGL(n,2) is 1/phi(m)*Sum_{d|m} mu(m/d)*b(n,d), where b(n,d) is number of solutions to x^d=1 in AGL(n,2).

Crossrefs

Formula

a(n) = (A063386(n)-1)/2.

A063413 Number of cyclic subgroups of order 10 of general affine group AGL(n,2).

Original entry on oeis.org

0, 0, 0, 0, 2666496, 8063483904, 23667221200896, 1546057323758223360, 374969260180817571741696, 163457085861840749434433961984, 112603564970401075916528447354044416, 152237556325944043707910988547266571141120, 824860715471760736216894023298196038268145893376
Offset: 1

Views

Author

Vladeta Jovovic, Jul 17 2001

Keywords

Comments

Number of cyclic subgroups of order m in general affine group AGL(n,2) is 1/phi(m)*Sum_{d|m} mu(m/d)*b(n,d), where b(n,d) is number of solutions to x^d=1 in AGL(n,2).

Crossrefs

Formula

a(n) = (A063393(n)-A063388(n)-A063385(n)+1)/4.

Extensions

More terms from Sean A. Irvine, Apr 23 2023

A053651 Number of nonisomorphic cyclic subgroups of general linear group GL(n,2).

Original entry on oeis.org

1, 3, 5, 8, 13, 18, 27, 37, 51, 70, 96, 130, 176, 232, 296, 380, 490, 620, 793, 1019, 1277, 1624
Offset: 1

Views

Author

Vladeta Jovovic, Mar 22 2000

Keywords

Examples

			a(5)=13 because the orders of the elements of GL(5,2) are {1,2,3,4,5,6,7,8,12,14,15,21,31}.
		

References

  • V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.

Crossrefs

Cf. A053658 (for GL(n,3)), A053660 (for GL(n, 4)).
Cf. A062766 (for AGL(n,2)).

Extensions

a(15)-a(22) from Sean A. Irvine, Jan 10 2022

A000214 Number of equivalence classes of Boolean functions of n variables under action of AG(n,2).

Original entry on oeis.org

3, 5, 10, 32, 382, 15768919, 16224999167506438730294, 84575066435667906978109556031081616704183639810103015118
Offset: 1

Views

Author

Keywords

Comments

AG denotes affine group.

References

  • V. Jovovic, The cycle indices polynomials of some classical groups, Belgrade, 1995, unpublished.
  • R. J. Lechner, Harmonic Analysis of Switching Functions, in A. Mukhopadhyay, ed., Recent Developments in Switching Theory, Ac Press, 1971, pp. 121-254, esp. p. 186.
  • 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).

Crossrefs

Cf. A000585.

Extensions

More terms from Vladeta Jovovic

A000585 Number of equivalence classes of Boolean functions of n variables under GL(n,2).

Original entry on oeis.org

4, 8, 20, 92, 2744, 950998216, 2076795963681989019155896, 21651217007530946175606768762255421159692845640522169779616
Offset: 1

Views

Author

Keywords

References

  • V. Jovovic, The cycle indices polynomials of some classical groups, Belgrade, 1995, unpublished.
  • R. J. Lechner, Harmonic Analysis of Switching Functions, in A. Mukhopadhyay, ed., Recent Developments in Switching Theory, Ac Press, 1971, pp. 121-254, esp. p. 186.
  • 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).

Extensions

More terms from Vladeta Jovovic

A062250 Number of cyclic subgroups of Chevalley group A_n(2) (the group of nonsingular n X n matrices over GF(2) ).

Original entry on oeis.org

1, 5, 79, 6974, 2037136, 2890467344, 14011554132032, 325330342132674560, 27173394819858612320256, 10158190320726534408118452224, 13156630408268153048253765001412608, 80280189722884518774834501142737770774528
Offset: 1

Views

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 01 2001

Keywords

Examples

			a(3) = 1/phi(1)+21/phi(2)+56/phi(3)+42/phi(4)+48/phi(7) = 79.
		

References

  • V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.

Crossrefs

Formula

a(n) = Sum_{d} |{g element of A_n(2): order(g)=d}|/phi(d), where phi=Euler totient function, cf. A000010.

Extensions

More terms from Vladeta Jovovic, Jul 04 2001

A063386 Number of solutions of x^3=1 in general affine group AGL(n,2).

Original entry on oeis.org

1, 9, 225, 6273, 968193, 307091457, 144510377985, 338450286215169, 1535613392752345089, 11693653105154832465921, 423384155808298738368118785, 29155340360444250715547947237377
Offset: 1

Views

Author

Vladeta Jovovic, Jul 16 2001

Keywords

Crossrefs

Showing 1-10 of 25 results. Next