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Triangle read by rows: T(n,k) = number of terms for the shortest Egyptian fraction representation of k/n, 1 <= k < n.
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%I #17 Jan 24 2017 02:39:14

%S 1,1,2,1,1,2,1,2,2,3,1,1,1,2,2,1,2,3,2,3,3,1,1,2,1,2,2,3,1,2,1,2,2,2,

%T 3,3,1,1,2,2,1,2,2,3,3,1,2,2,2,3,2,3,4,4,4,1,1,1,1,2,1,2,2,2,2,3,1,2,

%U 3,3,3,3,2,3,3,3,3,4,1,1,2,2,2,3,1,2,2,3,3,3,4,1,2,1,2,1,2,3,2,2,2,3,3,3,3

%N Triangle read by rows: T(n,k) = number of terms for the shortest Egyptian fraction representation of k/n, 1 <= k < n.

%C Not same as A050205. Example: the fraction 9/20 requires three terms in its greedy expansion, but 9/20 = 1/4 + 1/5, so T(20,9) = 2.

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

%e The triangle T(n,k) begins:

%e 2: 1

%e 3: 1 2

%e 4: 1 1 2

%e 5: 1 2 2 3

%e 6: 1 1 1 2 2

%e 7: 1 2 3 2 3 3

%e 8: 1 1 2 1 2 2 3

%e 9: 1 2 1 2 2 2 3 3

%Y Cf. A281527.

%K nonn,tabl

%O 2,3

%A _Arkadiusz Wesolowski_, Jan 23 2017