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 A277564 Let {c(i)} = A007916 denote the sequence of numbers > 1 which are not perfect powers. Every positive integer n has a unique representation as a tower n = c(x_1)^c(x_2)^c(x_3)^...^c(x_k), where the exponents are nested from the right. The sequence is an irregular triangle read by rows, where the n-th row lists n followed by x_1, ..., x_k. 14
 1, 2, 1, 3, 2, 4, 1, 1, 5, 3, 6, 4, 7, 5, 8, 1, 2, 9, 2, 1, 10, 6, 11, 7, 12, 8, 13, 9, 14, 10, 15, 11, 16, 1, 1, 1, 17, 12, 18, 13, 19, 14, 20, 15, 21, 16, 22, 17, 23, 18, 24, 19, 25, 3, 1, 26, 20, 27, 2, 2, 28, 21, 29, 22, 30, 23, 31, 24, 32, 1, 3, 33, 25, 34, 26, 35, 27, 36, 4, 1, 37, 28, 38, 29, 39, 30, 40, 31 (list; graph; refs; listen; history; text; internal format)