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Irregular triangle read by rows: strictly decreasing positive integer sequences in lexicographic order with the property that the sum of inverses is an integer.
4

%I #13 Apr 30 2016 17:17:59

%S 1,6,3,2,6,3,2,1,12,6,4,2,12,6,4,2,1,15,10,3,2,15,10,3,2,1,15,12,10,4,

%T 2,15,12,10,4,2,1,15,12,10,6,4,3,15,12,10,6,4,3,1,18,9,3,2,18,9,3,2,1,

%U 18,12,9,4,2,18,12,9,4,2,1,18,12,9,6,4,3,18,12

%N Irregular triangle read by rows: strictly decreasing positive integer sequences in lexicographic order with the property that the sum of inverses is an integer.

%H Peter Kagey, <a href="/A272082/b272082.txt">Table of n, a(n) for n = 1..4039</a> (All rows with first term less than or equal to 30.)

%e First 8 rows:

%e [1] because 1/1 is an integer

%e [6, 3, 2] because 1/6 + 1/3 + 1/2 = 1.

%e [6, 3, 2, 1] because 1/6 + 1/3 + 1/2 + 1/1 = 2.

%e [12, 6, 4, 2] because 1/12 + 1/6 + 1/4 + 1/2 = 1.

%e [12, 6, 4, 2, 1] because 1/12 + 1/6 + 1/4 + 1/2 + 1/1 = 2.

%e [15, 10, 3, 2] because 1/15 + 1/10 + 1/3 + 1/2 = 1.

%e [15, 10, 3, 2, 1] because 1/15 + 1/10 + 1/3 + 1/2 + 1/1 = 2.

%e [15, 12, 10, 4, 2] because 1/15 + 1/12 + 1/10 + 1/4 + 1/2 = 1.

%Y Cf. A272020, A272035, A272081, A272083.

%K nonn,tabf

%O 1,2

%A _Peter Kagey_, Apr 19 2016