The solvability of an arithmetic function equation related to pentagon number
By using the definition and properties of Smarandache function S(n),Smarandache LCM function SL(n)and generalized Euler function φ2(n),the solvability problems of arithmetic function equations S(SL(n23))=kφ2[n(3n-1)/2]related to pentagon number are studied,in which k∈Z+(Z+is a set of positive integers).The results are as follows:all positive integer solutions of the arithmetic function equations S(SL(n23)=kφ2[n(3n-1)/2]are(k,n)=(13,2),(2,12),(1,27).
Smarandache function S(n)Smarandache LCM function SL(n)generalized Euler functionφ2(n)pentagonal numberspositive integer solution
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