OFFSET
1,2
REFERENCES
Krassimir T. Atanassov, On the 43rd and 44th Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5, No. 2 (1999), 86-88.
J. Castillo, Other Smarandache Type Functions: Inferior/Superior Smarandache f-part of x, Smarandache Notions Journal, Vol. 10, No. 1-2-3 (1999), 202-204.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Krassimir T. Atanassov, On Some of Smarandache's Problems.
Li Jie, On the inferior and superior factorial part sequences, in Zhang Wenpeng (ed.), Research on Smarandache Problems in Number Theory (collected papers), 2004, pp. 47-48.
Florentin Smarandache, Only Problems, Not Solutions!.
FORMULA
n log log n / log n << a(n) <= n. - Charles R Greathouse IV, Sep 19 2012
From Amiram Eldar, Aug 02 2022: (Start)
Sum_{n>=1} 1/a(n)^m = Sum_{k>=1} k/k!^m (Li Jie, 2004).
In particular:
Sum_{n>=1} 1/a(n)^2 = e (A001113).
Sum_{n>=1} 1/a(n)^3 = BesselI(1,2) (A096789). (End)
MATHEMATICA
Table[k = 1; While[(k + 1)! <= n, k++]; k!, {n, 80}] (* Michael De Vlieger, Aug 30 2016 *)
PROG
(PARI) a(n)=my(t=1, k=1); while(t<=n, t*=k++); t/k \\ Charles R Greathouse IV, Sep 19 2012
(Python)
from sympy import factorial as f
def a(n):
k=1
while f(k + 1)<=n: k+=1
return f(k)
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 21 2017, after Mathematica code
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Charles T. Le (charlestle(AT)yahoo.com)
STATUS
approved