Putin and Solzhenitsyn very publicly agreed that Stalin was a ruthless madman who pulled Russia up by it's bootstraps but who also slaughtered millions of Russians for no reason (only a Russian could think, "on the one hand, but on the other . . .", about Stalin).
They also very publicly agreed Russia has a destiny that requires authoritarian leadership, Christian values, and predominently Slavic citizens, to fulfill. That's why Putin asked lawmakers in Russia to make Solzhenitsyn required reading in High Schools and they did so.
Putin rides propaganda about him being like Stalin to a lot of little victories, though, so I'm sure he doesn't mind a bit.