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A294721 Irregular triangle read by rows: T(n,k) = n if k is the largest divisor of n <= sqrt(n), otherwise T(n,k) = 0. The first element of column k is in row k^2, n>=1, k>=1.

%I A294721 #23 Nov 09 2017 22:01:54
%S A294721 1,2,3,0,4,5,0,0,6,7,0,0,8,0,0,9,0,10,0,11,0,0,0,0,12,13,0,0,0,14,0,0,
%T A294721 0,15,0,0,0,16,17,0,0,0,0,0,18,0,19,0,0,0,0,0,0,20,0,0,21,0,0,22,0,0,
%U A294721 23,0,0,0,0,0,0,24,0,0,0,0,25,0,26,0,0,0,0,0,27,0,0,0,0,0,28,0,29,0,0,0,0,0,0,0,0,30
%N A294721 Irregular triangle read by rows: T(n,k) = n if k is the largest divisor of n <= sqrt(n), otherwise T(n,k) = 0. The first element of column k is in row k^2, n>=1, k>=1.
%H A294721 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv06.jpg"> Illustration of initial terms</a>
%F A294721 T(n, A033676(n)) = n.
%F A294721 T(n,k) = 0, if k is not equal to A033676(n), n >= 1, and 1 <= k <= A000196(n).
%F A294721 T(n,k) = n*A294821(n,k).
%e A294721 Triangle begins:
%e A294721 1;
%e A294721 2;
%e A294721 3;
%e A294721 0,   4;
%e A294721 5,   0;
%e A294721 0,   6;
%e A294721 7,   0;
%e A294721 0,   8;
%e A294721 0,   0,   9;
%e A294721 0,  10,   0;
%e A294721 11,  0,   0;
%e A294721 0,   0,  12;
%e A294721 13,  0,   0;
%e A294721 0,  14,   0;
%e A294721 0,   0,  15;
%e A294721 0,   0,   0,  16;
%e A294721 17,  0,   0,   0;
%e A294721 0,   0,  18,   0;
%e A294721 19,  0,   0,   0;
%e A294721 0,   0,   0,  20;
%e A294721 0,   0,  21,   0;
%e A294721 0,  22,   0,   0;
%e A294721 23,  0,   0,   0;
%e A294721 0,   0,   0,  24;
%e A294721 0,   0,   0,   0,  25;
%e A294721 ...
%Y A294721 Cf. A033676, A163280, A294821.
%Y A294721 Row n has length A000196(n).
%Y A294721 Row sums give A000027.
%Y A294721 Positive terms also give A000027.
%Y A294721 Positive terms of column k, for k = 1..12, give respectively: A008578, A161344, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532.
%K A294721 nonn,tabf
%O A294721 1,2
%A A294721 _Omar E. Pol_, Nov 07 2017