Journal of Jianghan University(Natural Science Edition) ›› 2016, Vol. 44 ›› Issue (1): 18-21.doi: 10.16389/j.cnki.cn42-1737/n.2016.01.003

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Solvability of Arithmetic Function Equation S ( SL ( n ) ) = φ2( n )

ZHANG Lixia，ZHAO Xiqing，GUO Rui   

  1. School of Mathematics and Computer Science，Yan′an University，Yan′an 716000，Shanxi，China
  • Online:2016-02-28 Published:2016-03-11

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Abstract: For any positive integer n ，S( n ) ，SL( n ) ，φ2( n ) are Smarandache function，Smarandache LCM function and generalized Euler function. In the present paper， the solvability of equation S ( SL ( n ) )=φ2( n ) was studied and all the positive integer solutions n = 20，24，25，32，36，50，54 of the equation were given with the property of S( n ) ，SL( n ) ，φ2( n ) and elementary method.

Key words: Smarandache function, Smarandache LCM function, generalized Euler function, positive integer solutions

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