login
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.
15

%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