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.

A181861 a(n) = gcd(n^2, n!/floor(n/2)!^2).

Original entry on oeis.org

1, 1, 2, 3, 2, 5, 4, 7, 2, 9, 4, 11, 12, 13, 4, 45, 2, 17, 4, 19, 4, 21, 4, 23, 4, 25, 4, 27, 8, 29, 180, 31, 2, 99, 4, 175, 12, 37, 4, 117, 20, 41, 12, 43, 8, 675, 4, 47, 36, 49, 4, 153, 8, 53, 4, 55, 56, 57, 4, 59, 16
Offset: 0

Views

Author

Peter Luschny, Nov 21 2010

Keywords

Links

Crossrefs

Cf. A170826, A181860, A056040, A000290.

Programs

  • Magma
    [Gcd(n^2, Floor(Factorial(n)/(Factorial(Floor(n/2))^2))):n in [0..60]]; // Marius A. Burtea, Aug 03 2019
  • Maple
    A181861 := n -> igcd(n^2,n!/iquo(n,2)!^2);
  • Mathematica
    sf[n_] := n!/Quotient[n, 2]!^2; Table[GCD[n^2, sf[n]], {n, 0, 60}] (* Jean-François Alcover, Jun 28 2013 *)
  • PARI
    a(n)=gcd(n!/(n\2)!^2,n^2) \\ Charles R Greathouse IV, Feb 01 2013

Formula

a(n) = gcd(A000290(n), A056040(n)).

A181857 a(n) = lcm(n^2, n!).

Original entry on oeis.org

0, 1, 4, 18, 48, 600, 720, 35280, 40320, 362880, 3628800, 439084800, 479001600, 80951270400, 87178291200, 1307674368000, 20922789888000, 6046686277632000, 6402373705728000, 2311256907767808000, 2432902008176640000, 51090942171709440000, 1124000727777607680000
Offset: 0

Views

Author

Peter Luschny, Nov 21 2010

Keywords

Comments

If n > 4 then a(n) = n! for composite n and n * n! for prime n. - David A. Corneth, Aug 04 2015

Links

Crossrefs

Cf. A170826, A181860, A056040, A000290, A014973.

Programs

Formula

a(n) = lcm(A000290(n), A000142(n)).
a(n) = n! * A014973(n) for n >= 1. - Johannes W. Meijer, Jun 04 2016

A181858 a(n) = lcm(n^2, n!) / lcm(n^2, swinging_factorial(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 4, 4, 36, 18, 64, 576, 14400, 43200, 518400, 518400, 5080320, 12700800, 1625702400, 1625702400, 131681894400, 131681894400, 627056640000, 13168189440000, 1593350922240000
Offset: 0

Views

Author

Peter Luschny, Nov 21 2010

Keywords

Comments

A divisibility sequence, i.e., if m|n then a(m)|a(n). Except for n = 9 the prime factors of A181858(n) are the primes <= floor((n-1)/2). Using this fact the divisibility property can be proved. - Peter Luschny, Jan 10 2011

Links

Crossrefs

Cf. A000290, A056040, A170826, A181857, A181860.

Programs

  • Maple
    A181858 := n -> `if`(n=0, 1, ilcm(n^2,n!)/ilcm(n^2,n!/iquo(n,2)!^2));
  • Mathematica
    a[n_] := If[n == 0, 1, LCM[n^2, n!]/LCM[n^2, n!/Quotient[n, 2]!^2]];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jun 18 2019 *)
  • PARI
    a(n)=lcm(n^2,n!)/lcm(n!/(n\2)!^2,n^2) \\ Charles R Greathouse IV, Feb 01 2013

Formula

a(n) = A181857(n) / A181860(n).

A181859 a(n) = gcd(n^2, n!) / gcd(n^2, n!/floor(n/2)!^2).

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 9, 1, 32, 9, 25, 1, 12, 1, 49, 5, 128, 1, 81, 1, 100, 21, 121, 1, 144, 25, 169, 27, 98, 1, 5, 1, 512, 11, 289, 7, 108, 1, 361, 13, 80, 1, 147, 1, 242, 3, 529, 1, 64, 49, 625, 17, 338, 1, 729, 55, 56, 57
Offset: 0

Views

Author

Peter Luschny, Nov 21 2010

Keywords

Crossrefs

Cf. A170826, A181860, A056040, A000290.

Programs

  • Maple
    A181859 := n -> igcd(n^2,n!)/igcd(n^2,n!/iquo(n,2)!^2);
  • Mathematica
    a[n_] := GCD[n^2, n!]/GCD[n^2, n!/Quotient[n, 2]!^2];
Table[a[n], {n, 0, 57}] (* Jean-François Alcover, Jun 18 2019 *)
  • PARI
    a(n)=if(isprime(n), n, if(n==4, 8, n^2))/gcd(n^2,n!/(n\2)!^2) \\ Charles R Greathouse IV, Feb 01 2013

Formula

a(n) = A170826(n) / A181861(n).
Showing 1-4 of 4 results.

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