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- W2963502021 abstract "In [1] we define SMARANDACHE FACTOR PARTITION FUNCTION (SFP), as follows: Let <X1, <X2 , <X3 , ... <Xr be a set of r natural numbers and P1, P2, P3 I· • ·Pr be arbitrarily chosen distinct primes then F(<X1 1 <X2 1 <X3 1 ••• <Xr ) called the Smarandache Factor Partition of . (<X1 1 <X2 , <X3 1 ••• <Xr ) is defined as the number of ways in which the number a1 a2 a3 ar N = Pr could be expressed as the product of its' divisors. For simplicity, we denote F(<X1 , <X2 , <X3 , .. . . <Xr ) = F (N) ,where 0.1 0.2 0.3 a. r a.n N = P1 P2 P3 Pr Pn and pr is the rth prime. P1 =2, P2 = 3 etc. In this note another result pertaining to SFPs has been derived. DISCUSSION: Let a.r N = Pr (1) L(N) = length of that factor partition of N which contains the maximum number of terms. In this case we have 280 r L(N) = L Uj i= 1 (2) AL(N) = A set of L(N) distinct primes. (3) B(N) = { p: piN, p is a prime. } B (N) = { Pl·, P2 , ... Pr } (4) !'[ N, AL(N)] = {x I d(x) = Nand B(x) c AL(N) } , whered(x) is the number of divisors of x. To derive an expression for the order of the set '¥[ N, AL(NJl defined above. There are F'(N) factor partitions of N. Let F1 be one of them. F 1 -----~ N = Sl X S2 X S3 X ... X St. if" @default.
- W2963502021 created "2019-07-30" @default.
- W2963502021 creator A5005055343 @default.
- W2963502021 date "2014-03-01" @default.
- W2963502021 modified "2023-09-23" @default.
- W2963502021 title "Some More Ideas on Smarandache Factor Partitions" @default.
- W2963502021 hasPublicationYear "2014" @default.
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