At Loggerheads With Log-recursions!

logn(nTn)=logn+1Tn+1 \log_n (n T_n) = \log_{n+1} T_{n+1}

Consider a sequence of positive integers given by 1=T2,T3,T4, 1 = T_2, T_3, T_4, \ldots that satisfy the above recurrence relation. What is the number of factors of T100 T_{100} ?

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