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Triangle read by rows: T(n,k) = minimal number of terms needed to write k/n (for 1 <= k <= n with gcd(k,n) = 1) as a sum of unit fractions.
6

%I #6 Mar 31 2012 20:17:55

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

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

%U 2,3,3,3,1,2,2,3,2,3,3,4,1,2,2,3,3,2,3,4,2,3,3,3,3,4,4,5,1,2,2

%N Triangle read by rows: T(n,k) = minimal number of terms needed to write k/n (for 1 <= k <= n with gcd(k,n) = 1) as a sum of unit fractions.

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

%e Triangle begins:

%e 1

%e 1

%e 1 2

%e 1 2

%e 1 2 2 3

%e 1 2

%e 1 2 3 2 3 3

%e 1 2 2 3

%e 1 2 2 2 3 3

%e 1 2 2 3

%e 1 2 2 2 3 2 3 4 4 4

%e 1 2 2 3

%e 1 2 3 3 3 3 2 3 3 3 3 4

%e 1 2 2 2 3 4

%Y Cf. A097847, A097849.

%K nonn,tabf

%O 1,4

%A _Franklin T. Adams-Watters_, Aug 31 2004