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%I #17 Apr 30 2016 23:15:43
%S 1,2,3,4,5,6,6,3,6,3,2,7,8,9,10,11,12,12,4,12,6,12,6,4,12,6,4,2,13,14,
%T 15,15,10,15,10,3,15,10,3,2,15,10,6,15,12,10,15,12,10,4,15,12,10,4,2,
%U 15,12,10,6,4,3,16,17,18,18,9,18,9,3,18,9,3,2,18,9
%N Irregular triangle read by rows: strictly decreasing positive integer sequences in lexicographic order with the property that the sum of inverses is the inverse of an integer.
%H Peter Kagey, <a href="/A272081/b272081.txt">Table of n, a(n) for n = 1..2170</a> (All rows with first term less than or equal to 30.)
%e First 18 rows:
%e [1] because 1 is self-inverse.
%e [2] because 1/2 is the inverse of an integer.
%e [3]
%e [4] (...)
%e [5]
%e [6]
%e [6, 3] because 1/6 + 1/3 = 1/2.
%e [6, 3, 2] because 1/6 + 1/3 + 1/2 = 1/1.
%e [7]
%e [8]
%e [9] (...)
%e [10]
%e [11]
%e [12]
%e [12, 4] because 1/12 + 1/4 = 1/3.
%e [12, 6] because 1/12 + 1/6 = 1/4.
%e [12, 6, 4] because 1/12 + 1/6 + 1/4 = 1/2.
%e [12, 6, 4, 2] because 1/12 + 1/6 + 1/4 + 1/2 = 1/1.
%Y Cf. A272020, A272034, A272082, A272083.
%K nonn,tabf
%O 1,2
%A _Peter Kagey_, Apr 19 2016
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