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A111809 Triangle read by rows: for T(n,k), 1<=k<=n, gcd(k,n)=1, consider all representations of k/n as an Egyptian fraction; T(n,k) = minimal value of sum of denominators.

%I A111809 #12 Aug 23 2025 23:14:28
%S A111809 1,2,3,8,4,6,5,18,12,17,6,5,7,32,39,16,23,36,8,12,10,14,9,24,12,20,17,
%T A111809 23,10,15,7,20,11,72,48,36,47,24,35,95,72,60,12,10,7,12,13,98,71,82,
%U A111809 95,101,28,41,47,58,71,96,14,21,34,9,34,41,15,32,16,21,8,23,13,15,16,24,20
%N A111809 Triangle read by rows: for T(n,k), 1<=k<=n, gcd(k,n)=1, consider all representations of k/n as an Egyptian fraction; T(n,k) = minimal value of sum of denominators.
%C A111809 Row n has A000010(n) members. - _David Wasserman_, Mar 03 2009
%D A111809 Franklin T. Adams-Watters, Posting to Seq Fan mailing list, Aug 21 2004
%H A111809 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e A111809 Triangle begins:
%e A111809   1
%e A111809   2
%e A111809   3 8
%e A111809   4 6
%e A111809   5 18 12 17
%e A111809   6 5
%e A111809   7 32 39 16 23 36
%e A111809   8 12 10 14
%e A111809   9 24 12 20 17 23
%e A111809   10 15 7 20
%e A111809   11 72 48 36 47 24 35 95 72 60
%e A111809   12 10 7 12
%Y A111809 Cf. A097847, A097848, A097849, A111807, A111804, A111860.
%K A111809 nonn,tabf,changed
%O A111809 1,2
%A A111809 _N. J. A. Sloane_, based on communications from _Franklin T. Adams-Watters_, Nov 22 2005
%E A111809 Corrected and extended by _David Wasserman_, Mar 03 2009
%E A111809 T(15, 14) corrected by _David Wasserman_, Mar 19 2009