cp's OEIS Frontend

A228814 Triangle read by rows T(n,k), n>=1, k>=1, in which column k starts in row A002620(k+1). If k is odd the column k lists j's interleaved with (k-1)/2 zeros, where j = (k+1)/2. Otherwise, if k is even the column k lists the positive integers but starting from k/2+1, interleaved with (k-2)/2 zeros.

%I A228814 #34 Mar 14 2015 00:23:54
%S A228814 1,1,2,1,3,1,4,2,1,5,0,1,6,2,3,1,7,0,0,1,8,2,4,1,9,0,0,3,1,10,2,5,0,1,
%T A228814 11,0,0,0,1,12,2,6,3,4,1,13,0,0,0,0,1,14,2,7,0,0,1,15,0,0,3,5,1,16,2,
%U A228814 8,0,0,4,1,17,0,0,0,0,0,1,18,2,9,3,6,0
%N A228814 Triangle read by rows T(n,k), n>=1, k>=1, in which column k starts in row A002620(k+1). If k is odd the column k lists j's interleaved with (k-1)/2 zeros, where j = (k+1)/2. Otherwise, if k is even the column k lists the positive integers but starting from k/2+1, interleaved with (k-2)/2 zeros.
%C A228814 The number of positive terms of row n is A000005(n).
%C A228814 The positive terms of row n are the divisors of n.
%C A228814 The number of zeros in row n equals A078152(n).
%C A228814 Row n has length A055086(n).
%C A228814 The sum of row n is A000203(n).
%C A228814 Positive terms give A210959.
%C A228814 It appears that there are only eight rows that do not contain zeros. The indices of these rows are 1, 2, 3, 4, 6, 8, 12, 24, the divisors of 24, see A018253.
%C A228814 For another version see A228812.
%e A228814 For n = 60 the 60th row of triangle is [1, 60, 2, 30, 3, 20, 4, 15, 5, 12, 6, 10, 0, 0]. The row length is A055086(60) = 14. The number of zeros is A078152(60) = 2. The number of positive terms is A000005(60) = 12. The row sum is A000203(60) = 168.
%e A228814 Triangle begins:
%e A228814 1;
%e A228814 1,  2;
%e A228814 1,  3;
%e A228814 1,  4,  2;
%e A228814 1,  5,  0;
%e A228814 1,  6,  2,  3;
%e A228814 1,  7,  0,  0;
%e A228814 1,  8,  2,  4;
%e A228814 1,  9,  0,  0,  3;
%e A228814 1, 10,  2,  5,  0;
%e A228814 1, 11,  0,  0,  0;
%e A228814 1, 12,  2,  6,  3,  4;
%e A228814 1, 13,  0,  0,  0,  0;
%e A228814 1, 14,  2,  7,  0,  0;
%e A228814 1, 15,  0,  0,  3,  5;
%e A228814 1, 16,  2,  8,  0,  0,  4;
%e A228814 1, 17,  0,  0,  0,  0,  0;
%e A228814 1, 18,  2,  9,  3,  6,  0;
%e A228814 1, 19,  0,  0,  0,  0,  0;
%e A228814 1, 20,  2, 10,  0,  0,  4,  5;
%e A228814 1, 21,  0,  0,  3,  7,  0,  0;
%e A228814 1, 22,  2, 11,  0,  0,  0,  0;
%e A228814 1, 23,  0,  0,  0,  0,  0,  0;
%e A228814 1, 24,  2, 12,  3,  8,  4,  6;
%e A228814 ...
%Y A228814 Column 1 is A000012.
%Y A228814 Cf. A000005, A000203, A002620, A004526, A018253, A027750, A055086, A078152, A147861, A161904, A196020, A210959, A212119, A212120, A221645, A228812, A228813, A229940, A229942, A228944, A229950, A228951.
%K A228814 nonn,tabf
%O A228814 1,3
%A A228814 _Omar E. Pol_, Oct 03 2013