cp's OEIS Frontend

A272025 Irregular triangle read by rows, n >= 1, 1 <= k <= A038548(n), in which T(n,k) is the sum of the k-th pair of conjugate divisors of n, or T(n,k) is the central divisor of n if such a pair does not exist.

%I A272025 #31 Jun 13 2021 03:25:16
%S A272025 1,3,4,5,2,6,7,5,8,9,6,10,3,11,7,12,13,8,7,14,15,9,16,8,17,10,4,18,19,
%T A272025 11,9,20,21,12,9,22,10,23,13,24,25,14,11,10,26,5,27,15,28,12,29,16,11,
%U A272025 30,31,17,13,11,32,33,18,12,34,14,35,19,36,12,37,20,15,13,6,38,39,21,40,16,41,22,14,13,42,43,23,17,13
%N A272025 Irregular triangle read by rows, n >= 1, 1 <= k <= A038548(n), in which T(n,k) is the sum of the k-th pair of conjugate divisors of n, or T(n,k) is the central divisor of n if such a pair does not exist.
%H A272025 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/poldiv05.jpg">Illustration of the divisors of the first 12 positive integers</a>
%H A272025 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A272025 Triangle begins:
%e A272025   1;
%e A272025   3;
%e A272025   4;
%e A272025   5, 2;
%e A272025   6;
%e A272025   7, 5;
%e A272025   8;
%e A272025   9, 6;
%e A272025   10, 3;
%e A272025   11, 7;
%e A272025   12;
%e A272025   13, 8, 7;
%e A272025   ...
%e A272025 For n = 9 the divisors of 9 are [1, 3, 9]. There is only one pair of conjugate divisors: [1, 9], and the central divisor is 3, so the 9th row of the triangle is [10, 3].
%e A272025 For n = 12 the divisors of 12 are [1, 2, 3, 4, 6, 12]. There are three pairs of conjugate divisors, they are [1, 12], [2, 6], [3, 4], so the 12th row of the triangle is [13, 8, 7].
%Y A272025 Row sums give A000203.
%Y A272025 Row lengths give A038548.
%Y A272025 Right border gives A207376.
%Y A272025 Column 1 is A065475.
%Y A272025 Cf. A027750, A210959, A228814.
%K A272025 nonn,tabf
%O A272025 1,2
%A A272025 _Omar E. Pol_, Apr 21 2016