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a(n) = (ceiling (sqrt(n)))!.
5

%I #30 Jan 20 2024 11:29:06

%S 1,1,2,2,2,6,6,6,6,6,24,24,24,24,24,24,24,120,120,120,120,120,120,120,

%T 120,120,720,720,720,720,720,720,720,720,720,720,720,5040,5040,5040,

%U 5040,5040,5040,5040,5040,5040,5040,5040,5040,5040,40320,40320,40320

%N a(n) = (ceiling (sqrt(n)))!.

%H Vincenzo Librandi, <a href="/A214078/b214078.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A000142(A003059(n)). - _Michel Marcus_, Jul 28 2022

%F Sum_{n>=0} 1/a(n) = e + 2. - _Amiram Eldar_, Aug 15 2022

%t Table[Ceiling[Sqrt[n]]!, {n, 0, 50}] (* _T. D. Noe_, Dec 23 2012 *)

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

%o (Magma) [Factorial(Ceiling (Sqrt(n))): n in [0..50]]; // _Vincenzo Librandi_, Feb 13 2013

%o (PARI) a(n) = ceil(sqrt(n))!; \\ _Altug Alkan_, Jan 11 2016

%o (Python)

%o from math import factorial, isqrt

%o def A214078(n): return factorial(1+isqrt(n-1)) if n else 1 # _Chai Wah Wu_, Jul 28 2022

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

%Y Cf. A000142, A003059.

%K easy,nonn

%O 0,3

%A _Mohammad K. Azarian_, Dec 22 2012