A214080 -id:A214080 - cp's OEIS frontend

A214083 a(n) = floor(n!^(1/3)).

1, 1, 1, 1, 2, 4, 8, 17, 34, 71, 153, 341, 782, 1839, 4434, 10935, 27555, 70852, 185686, 495486, 1344956, 3710632, 10397338, 29568648, 85290741, 249391641, 738821756, 2216465268, 6730493989, 20678209929, 64252006059, 201840008711, 640802084315

Offset: 0

Mohammad K. Azarian, Dec 22 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

PROG(y := [], n := 35, LOOP(IF(n = -1, RETURN y), y := ADJOIN(FLOOR(n!^(1/3)), y), n := n - 1))

[Floor(Factorial(n)^(1/3)): n in [0..40]]; // Vincenzo Librandi, Feb 08 2013

Table[Floor[n!^(1/3)], {n, 0, 60}] (* Vincenzo Librandi, Feb 08 2013 *)

a(n) = sqrtnint(n!,3); \\ Michel Marcus, Jan 11 2016

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

Mohammad K. Azarian, Dec 22 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Cf. A000142, A003059.

PROG(y := [], n := 50, LOOP(IF(n = -1, RETURN y), y := ADJOIN(CEILING(SQRT(n))!, y), n := n - 1))

[Factorial(Ceiling (Sqrt(n))): n in [0..50]]; // Vincenzo Librandi, Feb 13 2013

Table[Ceiling[Sqrt[n]]!, {n, 0, 50}] (* T. D. Noe, Dec 23 2012 *)

a(n) = ceil(sqrt(n))!; \\ Altug Alkan, Jan 11 2016

from math import factorial, isqrt
def A214078(n): return factorial(1+isqrt(n-1)) if n else 1 # Chai Wah Wu, Jul 28 2022

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

Mohammad K. Azarian, Dec 22 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Cf. A000142, A134914.

PROG(y := [], x := 70, LOOP(IF(x = -1, RETURN y), y := ADJOIN(CEILING(x^(1/3))!, y), x := x - 1))

[Factorial(Ceiling(n^(1/3))): n in [0..80]]; // Vincenzo Librandi, Feb 13 2013

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 *)

a(n) = ceil(n^(1/3))! \\ Altug Alkan, Jan 11 2016

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

Mohammad K. Azarian, Dec 22 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Cf. A000142, A048766.

PROG(y := [], n := 70, LOOP(IF(n = -1, RETURN y), y := ADJOIN(FLOOR(n^(1/3))!, y), n := n - 1))

[Factorial(Floor(n^(1/3))): n in [0..80]]; // Vincenzo Librandi, Feb 13 2013

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 *)

a(n) = floor(n^(1/3))!; \\ Altug Alkan, Jan 11 2016

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

a(n) = A000142(A048766(n)). - Michel Marcus, Aug 15 2022

A228729 Product of the positive squares less than or equal to n.

Original entry on oeis.org

1, 1, 1, 4, 4, 4, 4, 4, 36, 36, 36, 36, 36, 36, 36, 576, 576, 576, 576, 576, 576, 576, 576, 576, 14400, 14400, 14400, 14400, 14400, 14400, 14400, 14400, 14400, 14400, 14400, 518400, 518400, 518400, 518400, 518400, 518400, 518400, 518400, 518400, 518400

Offset: 1

Wesley Ivan Hurt, Aug 31 2013

Squares of A214080, n > 0. Also, the n-th value of A001044 (The squared factorial numbers) repeated 2n+1 times, n > 0.

The first differences of a(n) are positive when n is a square (i.e., a(n+1) - a(n) > 0) and zero otherwise. This implies that the square characteristic (A010052) can be written in terms of a(n) as A010052(n) = signum(a(n+1) - a(n)), n > 1. Furthermore, the number of squares less than or equal to n is given by Sum_{i=1..n} sign(a(i+1) - a(i)), and the sum of the squares less than or equal to n is given by Sum_{i=2..n} i * sign(a(i+1) - a(i)).

			a(6) = 4 since there are two squares less than or equal to 6 (1 and 4) and their product is 1*4 = 4.

Cf. A000290, A001044, A010052, A214080.

seq(product( (i)^(1 - ceil(sqrt(i)) + floor(sqrt(i))), i = 1..k ), k=1..100);

Table[Times@@(Range[Floor[Sqrt[n]]]^2), {n, 50}] (* Alonso del Arte, Sep 01 2013 *)

a(n) = Product_{i=1..n} i^(1 - ceiling(frac(sqrt(i)))).
a(n) = A214080(n)^2, n > 0.
Sum_{n>=1} 1/a(n) = BesselI(0, 2) + 2*BesselI(1, 2) - 1. - Amiram Eldar, Aug 15 2025

cp's OEIS Frontend

A214083 a(n) = floor(n!^(1/3)).

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

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

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

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A228729 Product of the positive squares less than or equal to n.

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