%I #11 Jun 18 2012 13:11:47

%S 2,3,4,5,2,2,6,3,2,7,4,2,3,3,8,5,2,4,3,9,6,2,5,3,2,2,2,10,7,2,4,4,6,3,

%T 3,2,2,11,8,2,5,4,7,3,4,2,2,12,9,2,6,4,3,3,2,8,3,5,2,2,5,5,13,10,2,7,

%U 4,4,3,2,9,3,6,2,2,6,5,14,11,2,8,4,5,3,2,3

%N Row n of table lists exponents in canonical prime factorization of A181800(n) (n-th powerful number that is the first integer of its prime signature), in nonincreasing order.

%C A212179(n) gives length of row n.

%C Table represents prime signature (cf. A212171) and second signature (cf. A212172) of A181800.

%H Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>

%F Row n is identical to row A181800(n) of tables A212171 and A212172.

%e Since 72 is a member of A181800, all positive exponents in its prime factorization (2^3*3^2) equal or exceed 2. Therefore, its second signature is the same as its prime signature, namely, {3,2} (nonincreasing version). Since 72 = A181800 (8), row 8 represents the prime signature and second signature {3,2}.

%Y Cf. A181800, A212171, A212172, A212179.

%K nonn,tabf

%O 2,1

%A _Matthew Vandermast_, Jun 03 2012