%I #36 Jun 17 2017 14:25:40
%S 1,2,1,1,3,4,5,1,2,2,1,6,7,8,9,10,11,1,1,1,12,13,14,15,16,17,18,19,3,
%T 1,20,2,2,21,22,23,24,1,3,25,26,27,4,1,28,29,30,31
%N 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 x_1, ..., x_k.
%C Row lengths are A288636(n). - _Gus Wiseman_, Jun 12 2017
%H N. J. A. Sloane, <a href="/A278028/b278028.txt">Table of n, a(n) for n = 1..20181</a>
%H N. J. A. Sloane, <a href="/A278028/a278028.txt">Maple programs for A007916, A278028, A278029, A052409, A089723, A277564</a>
%e Rows 2 through 32 are:
%e 1,
%e 2,
%e 1, 1,
%e 3,
%e 4,
%e 5,
%e 1, 2,
%e 2, 1,
%e 6,
%e 7,
%e 8,
%e 9,
%e 10,
%e 11,
%e 1, 1, 1,
%e 12,
%e 13,
%e 14,
%e 15,
%e 16,
%e 17,
%e 18,
%e 19,
%e 3, 1,
%e 20,
%e 2, 2,
%e 21,
%e 22,
%e 23,
%e 24,
%e 1, 3,
%e ...
%Y See A277564 for another version.
%Y Cf. A007916, A089723, A277562, A288636.
%K nonn,tabf
%O 1,2
%A _N. J. A. Sloane_, Nov 09 2016