cp's OEIS Frontend

A210959 Triangle read by rows in which row n lists the divisors of n starting with 1, n, the second smallest divisor of n, the second largest divisor of n, the third smallest divisor of n, the third largest divisor of n, and so on.

%I A210959 #26 Jun 20 2019 02:58:27
%S A210959 1,1,2,1,3,1,4,2,1,5,1,6,2,3,1,7,1,8,2,4,1,9,3,1,10,2,5,1,11,1,12,2,6,
%T A210959 3,4,1,13,1,14,2,7,1,15,3,5,1,16,2,8,4,1,17,1,18,2,9,3,6,1,19,1,20,2,
%U A210959 10,4,5,1,21,3,7,1,22,2,11,1,23,1,24
%N A210959 Triangle read by rows in which row n lists the divisors of n starting with 1, n, the second smallest divisor of n, the second largest divisor of n, the third smallest divisor of n, the third largest divisor of n, and so on.
%C A210959 A two-dimensional arrangement of squares has the property that the number of vertices in row n equals the number of divisors of n. So T(n,k) is represented in the structure as the k-th vertex of row n (see the illustration of initial terms).
%H A210959 Michel Marcus, <a href="/A210959/b210959.txt">Rows 1..1000, flattened</a>
%H A210959 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv11.jpg">Illustration of initial terms</a>
%H A210959 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A210959 Written as an irregular triangle the sequence begins:
%e A210959 1;
%e A210959 1, 2;
%e A210959 1, 3;
%e A210959 1, 4, 2;
%e A210959 1, 5;
%e A210959 1, 6, 2, 3;
%e A210959 1, 7;
%e A210959 1, 8, 2, 4;
%e A210959 1, 9, 3;
%e A210959 1, 10, 2, 5;
%e A210959 1, 11;
%e A210959 1, 12, 2, 6, 3, 4;
%o A210959 (PARI) row(n) = my(d=divisors(n)); vector(#d, k, if (k % 2, d[(k+1)/2], d[#d-k/2+1])); \\ _Michel Marcus_, Jun 20 2019
%Y A210959 Row n has length A000005(n). Row sums give A000203. Right border gives A033677.
%Y A210959 Cf. A027750, A161901, A212119.
%K A210959 nonn,tabf
%O A210959 1,3
%A A210959 _Omar E. Pol_, Jul 29 2012