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.

A259340 Erroneous version of A002826.

Original entry on oeis.org

1, 5, 18, 80, 667, 15237, 7854724
Offset: 1

Views

Author

N. J. A. Sloane, Jun 02 2017

Keywords

References

  • E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian) Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622.

Links

  • E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian), Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622. [Annotated scanned copy]

A246069 Number of maximal classes determined by permutations.

Original entry on oeis.org

0, 1, 1, 3, 6, 35, 120, 105, 1120, 19089, 362880, 133595, 39916800, 148397535, 458313856, 2027025, 1307674368000, 6133352225, 355687428096000, 40549021532019, 4139906028544000, 464463124401214575, 51090942171709440000, 1173011341727225
Offset: 1

Views

Author

Sean A. Irvine, Aug 25 2014

Keywords

Comments

Corresponds to r_2(k) in the Rosenberg paper.

Links

Crossrefs

Cf. A002826.

Programs

  • Maple
    a:= n -> add(n!/((n/p)! * p^(n/p) * (p-1)), p = numtheory:-factorset(n)):
seq(a(n), n=1..100); # Robert Israel, Aug 27 2014
  • Mathematica
    a[n_] := If[n == 1, 0, Sum[n!/((n/p)! p^(n/p) (p-1)), {p, FactorInteger[n][[All, 1]]}]]; Array[a, 100] (* Jean-François Alcover, Mar 22 2019, after Robert Israel *)

Formula

a(n) = sum(n! / (m! * p^m * (p-1)), n = p * m, p prime). (corrected by Robert Israel, Aug 27 2014)

A246137 Number of maximal classes determined by elementary Abelian p-groups.

Original entry on oeis.org

0, 1, 1, 1, 6, 0, 120, 30, 840, 0, 362880, 0, 39916800, 0, 0, 64864800, 1307674368000, 0, 355687428096000, 0, 0, 0, 51090942171709440000, 0, 1292600836944248832000, 0, 35905578804006912000000, 0
Offset: 1

Views

Author

Sean A. Irvine, Aug 25 2014

Keywords

Comments

Corresponds to r_3(k) in the Rosenberg paper.

Links

Crossrefs

Cf. A002826.

Formula

a(p^m) = (p^m-1)! / (p^binomial(m, 2) * (p-1) * (p^2-1) * ... * (p^m-1)). In all other cases a(n) = 0.

A246417 Homomorphic inverse images of elementary h-ary relations.

Original entry on oeis.org

0, 0, 1, 7, 36, 171, 813, 4012, 25931, 342263, 6498746, 116477549, 1839530421, 26071946330, 339710531761, 4165394873379, 50578180795388, 717354862704287, 15348610400624113, 466529833772501084, 15332096138370552335
Offset: 1

Views

Author

Sean A. Irvine, Aug 25 2014

Keywords

Comments

Corresponds to r_6(k) in the Rosenberg paper.

References

  • E. Ju. Zaharova, V. B. Kudrjavcev, and S. V. Jablonskii, Precomplete classes in k-valued logics. (Russian) Dokl. Akad. Nauk SSSR 186 (1969), 509-512. English translation in Soviet Math. Doklady 10 (No. 3, 1969), 618-622.

Links

Crossrefs

Cf. A002826.

Formula

a(n) = Sum_{h^m <= k, h >= 3, m >= 1} (((-1)^h / (m! * (h!)^m)) * Sum_{L=1..h^m} (-1)^L * binomial(h^m, L) * L^n). - Sean A. Irvine, Aug 25 2014
Showing 1-4 of 4 results.

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

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