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 1-5 of 5 results.

A214080 a(n) = (floor(sqrt(n)))!

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 24, 24, 24, 24, 24, 24, 24, 24, 24, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 720, 720, 720, 720, 720, 720, 720, 720, 720, 720, 720, 720, 720, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040
Offset: 0

Views

Author

Mohammad K. Azarian, Dec 22 2012

Keywords

Links

Crossrefs

Cf. A214078, A214079, A214080, A214081, A214083, A055228, A055226.
Cf. A000142, A000196.

Programs

  • Derive
    PROG(y := [], n := 50, LOOP(IF( = -1, RETURN y), y := ADJOIN(FLOOR(SQRT(n))!, y), n := n - 1))
  • Magma
    [Factorial(Floor(Sqrt(n))): n in [0..60]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Floor[Sqrt[n]]!, {n, 0, 100}] (* T. D. Noe, Dec 23 2012 *)
  • PARI
    a(n) = floor(sqrt(n))!; \\ Altug Alkan, Jan 11 2016

Formula

Sum_{n>=0} 1/a(n) = 3*e. - Amiram Eldar, Aug 15 2022
a(n) = A000142(A000196(n)). - Michel Marcus, Aug 15 2022

A214078 a(n) = (ceiling (sqrt(n)))!.

Original entry on oeis.org

1, 1, 2, 2, 2, 6, 6, 6, 6, 6, 24, 24, 24, 24, 24, 24, 24, 120, 120, 120, 120, 120, 120, 120, 120, 120, 720, 720, 720, 720, 720, 720, 720, 720, 720, 720, 720, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 40320, 40320, 40320
Offset: 0

Views

Author

Mohammad K. Azarian, Dec 22 2012

Keywords

Links

Crossrefs

Cf. A214078, A214079, A214080, A214081, A214083, A055228, A055226.
Cf. A000142, A003059.

Programs

  • Derive
    PROG(y := [], n := 50, LOOP(IF(n = -1, RETURN y), y := ADJOIN(CEILING(SQRT(n))!, y), n := n - 1))
  • Magma
    [Factorial(Ceiling (Sqrt(n))): n in [0..50]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Ceiling[Sqrt[n]]!, {n, 0, 50}] (* T. D. Noe, Dec 23 2012 *)
  • PARI
    a(n) = ceil(sqrt(n))!; \\ Altug Alkan, Jan 11 2016
  • Python
    from math import factorial, isqrt
def A214078(n): return factorial(1+isqrt(n-1)) if n else 1 # Chai Wah Wu, Jul 28 2022

Formula

a(n) = A000142(A003059(n)). - Michel Marcus, Jul 28 2022
Sum_{n>=0} 1/a(n) = e + 2. - Amiram Eldar, Aug 15 2022

A214079 a(n) = ceiling( n^(1/3) )!.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 120, 120, 120, 120, 120
Offset: 0

Views

Author

Mohammad K. Azarian, Dec 22 2012

Keywords

Links

Crossrefs

Cf. A214078, A214079, A214080, A214081, A214083, A055228, A055226.
Cf. A000142, A134914.

Programs

  • Derive
    PROG(y := [], x := 70, LOOP(IF(x = -1, RETURN y), y := ADJOIN(CEILING(x^(1/3))!, y), x := x - 1))
  • Magma
    [Factorial(Ceiling(n^(1/3))): n in [0..80]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Ceiling[n^(1/3)]!, {n, 0, 100}] (* T. D. Noe, Dec 23 2012 *)
Ceiling[Surd[Range[0,70],3]]! (* Harvey P. Dale, Nov 19 2022 *)
  • PARI
    a(n) = ceil(n^(1/3))! \\ Altug Alkan, Jan 11 2016

Formula

Sum_{n>=0} 1/a(n) = 4*e. - Amiram Eldar, Aug 15 2022
a(n) = A000142(A134914(n)). - Michel Marcus, Aug 15 2022

A214081 a(n) = floor( n^(1/3) )!.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24
Offset: 0

Views

Author

Mohammad K. Azarian, Dec 22 2012

Keywords

Links

Crossrefs

Cf. A055226, A055228, A214078, A214079, A214080, A214081, A214083.
Cf. A000142, A048766.

Programs

  • Derive
    PROG(y := [], n := 70, LOOP(IF(n = -1, RETURN y), y := ADJOIN(FLOOR(n^(1/3))!, y), n := n - 1))
  • Magma
    [Factorial(Floor(n^(1/3))): n in [0..80]]; // Vincenzo Librandi, Feb 13 2013
  • Mathematica
    Table[Floor[n^(1/3)]!, {n, 0, 100}] (* T. D. Noe, Dec 23 2012 *)
Floor[CubeRoot[Range[0,90]]]! (* Harvey P. Dale, Jan 15 2024 *)
  • PARI
    a(n) = floor(n^(1/3))!; \\ Altug Alkan, Jan 11 2016

Formula

Sum_{n>=0} 1/a(n) = 10*e. - Amiram Eldar, Aug 15 2022
a(n) = A000142(A048766(n)). - Michel Marcus, Aug 15 2022

A226973 Difference between n! and the largest cube < n!.

Original entry on oeis.org

1, 1, 5, 16, 56, 208, 127, 1016, 4969, 47223, 264979, 789832, 7668081, 4272696, 130217625, 883909125, 9969785792, 52152119144, 128092980744, 2166664965184, 29992267884032, 272465658461528, 1588888484126208, 10747891377020979, 5480400487212279, 70703132766750784, 1908984584702271168
Offset: 1

Views

Author

Zak Seidov, Jun 25 2013

Keywords

Comments

Also, smallest number k such that n! - k is a cube.
Sequence is not monotonic: a(n) < a(n-1) for n: 7, 14, 25, 30, 51, 106, 168, 279, 288.

Examples

			a(2) = 2! - 1^3 = 1, a(3) = 3! - 1^3 = 5, a(4) = 4! - 3^3 = 16.

Links

Crossrefs

Cf. A000142, A066857, A214083.

Programs

  • Mathematica
    Join[{1}, Table[n! - Floor[(n!)^(1/3)]^3, {n, 2, 30}]]
  • PARI
    a(n)=my(N=n!);N-sqrtnint(N,3)^3 \\ Charles R Greathouse IV, Jun 25 2013

Formula

a(n) = n! - floor (n!^(1/3))^3 = A000142(n) - A214083(n)^3.
Showing 1-5 of 5 results.

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