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A272081 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.

%I A272081 #17 Apr 30 2016 23:15:43
%S A272081 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 A272081 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 A272081 15,12,10,6,4,3,16,17,18,18,9,18,9,3,18,9,3,2,18,9
%N A272081 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 A272081 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 A272081 First 18 rows:
%e A272081   [1]           because 1 is self-inverse.
%e A272081   [2]           because 1/2 is the inverse of an integer.
%e A272081   [3]
%e A272081   [4]           (...)
%e A272081   [5]
%e A272081   [6]
%e A272081   [6, 3]        because 1/6 + 1/3              = 1/2.
%e A272081   [6, 3, 2]     because 1/6 + 1/3 + 1/2        = 1/1.
%e A272081   [7]
%e A272081   [8]
%e A272081   [9]           (...)
%e A272081   [10]
%e A272081   [11]
%e A272081   [12]
%e A272081   [12, 4]       because 1/12 + 1/4             = 1/3.
%e A272081   [12, 6]       because 1/12 + 1/6             = 1/4.
%e A272081   [12, 6, 4]    because 1/12 + 1/6 + 1/4       = 1/2.
%e A272081   [12, 6, 4, 2] because 1/12 + 1/6 + 1/4 + 1/2 = 1/1.
%Y A272081 Cf. A272020, A272034, A272082, A272083.
%K A272081 nonn,tabf
%O A272081 1,2
%A A272081 _Peter Kagey_, Apr 19 2016