A New Inequality for the Smarandache Function

1 Pages·1997·0.02 MB·

by  Mihaly Bencze

A NEW INEQUALITY FOR THE SMARANDACHE FUNCTION
Mihaly Bencze
Str. Hannanului 6
2212 Sacele 3, jUdo Brasov
Romania.
Theorem. Let SCm)=min {kE N: mi k!} be the Smarandache Function.
and a k , b k E N* (k=1,2, ... ,n), then we have the following inequality ,
b
n k
S(TI (a k ~)
lc=l
Proof:
n n
I,C a bJ~ TIC a bJ!
k k
k-I l..~1
*
b
n n k
TIC a bJ~ TI Cak~)
k
1.:=1 k-I 1.:=1
al bl -i- a2 b:; + ,., + am b m 'I I a 2 b 2 -+- ... ..:... a m b m \ / a m-l b m- 1 + a m b m\
(
a b ) \ a b a b
l I 2 2 ) ... \ m-I m-l )
3ak)\ (, 2a k\ \
a k ak I; E N*
From this result
k=1
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