[seqfan] a question to the experts regarding the product of tau-values for consecutive integers (A092517)

[Thomas Scheuerle]

I wish you a happy and successful New Year !

It appears that A092517(n) (number of divisors of n*(n+1)) equals
the number of bases b which allow to write (n+1)^2 as a sum
of n+1 summands of the form b^c_1 + b^c_2 + ... + b^c_(n+1).

Examples:  
2^2 = 2^1 + 2^1 = 3^0 + 3^1 -> 2,3 -> A092517(1) = 2.
3^2 = 2^2 + 2^2 + 2^0 = 3^1 + 3^1 + 3^1 = 4^1 + 4^1 + 4^0 = 7^1 + 7^0 + 7^0 -> 2,3,4,7 -> A092517(2) = 4.

Does there exist an easy explanation ?