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A080500
a(n) = (n-1)(n-4)(n-9)...(n-k^2) where k^2 < n <= (k+1)^2.
The idea of A080497 to A080500 when applied to Euler's phi function i.e. on phi-torial function defined in A001783 yields A001783 itself for obvious reasons. Is there any other such example?