id: 02344125
dt: j
an: 2002b.01328
au: Wu, Rex H.
ti: Some properties of the equation S(x)=k.
so: Pi Mu Epsilon J. 11, No. 5, 265-270 (2001).
py: 2001
pu: Worcester Polytechnic Institute (WPI), Mathematical Sciences, Worcester, MA
la: EN
cc: F60
ut:
ci:
li:
ab: In 1979, Florentin Smarandache introduced a number theoretic function. For
any positive integer n, the Smarandache function S(n) is defined as
S(n)=k if k is the smallest positive integer such that n divides k!.
Since then, some interesting properties have been discovered about this
function. Just one example, for $x>4$, the expression
$π$(x)=-1+$(Σ_{k=2}^x)\lbrackS(k)/k\rbrack$, where \lbrackx\rbrack is
the greatest integer function, gives the exact number of primes less
than or equal to x. In this note, we will look at some elementary
properties associated with the equations S(x)=k. (From the
introduction)
rv: