A NOTE ON THE SMARANDACHE DIVISOR SEQUENCES (Amarnath Murthy ,S.E. (E &T), Well Logging Services,Oil And Natural Gas Corporation Ltd. ,Sabarmati, Ahmedbad, India- 380005.)
ABSTRACT:
In
[1]
we
define
SMARANDACHE
FACTOR
PARTITION FUNCTION (SFP) , as follows: Let
CX1, CX2 , CX3 , . . . CX r be a set of r natural numbers
and P1, P2, P3 , .. 路Pr be
arbitrarily chosen distinct primes then
F(cx1' CX2 , CX3 , ... cx r ) called the Smarandache Factor Partition of (CX1, CX2 , CX3 ,.
. cx r ) is defined as the number of ways in which the
number a1
N
a2
a3
ar Pr
=
could be expressed as the
product of its' divisors. For simplicity, we denote F(cx1 , CX2 , CX3 , . CX r ) = F (N) ,where a1
N
ar
a3
0路.2
P1 P2 P3
=
an
Pr
Pn
and Pr is the rth prime. P1 =2, P2 = 3
etc.
In [2] we have defined SMARANDACHE DIVISOR SEQUENCES as follows
I d(x) =
Pn = { x
P2 = { x P3
I
={x I
P4 = { x
I
n}
,d(x)
= number of divisors
of n.
x is a prime} x
= p2,
P is a prime}
x = p3 or x = P1P2 , P ,P1 ,P2 are primes} 284