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A378912 Irregular triangle read by rows: row n lists all positive m such that sigma(m) divides n, where sigma is the sum-of-divisors function (A000203).

%I A378912 #22 Dec 12 2024 15:12:28
%S A378912 1,1,1,2,1,3,1,1,2,5,1,4,1,3,7,1,2,1,1,1,2,3,5,6,11,1,9,1,4,13,1,2,8,
%T A378912 1,3,7,1,1,2,5,10,17,1,1,3,19,1,2,4,1,1,1,2,3,5,6,7,11,14,15,23,1,1,9,
%U A378912 1,2,1,3,4,12,13,1,1,2,5,8,29,1,16,25,1,3,7,21,31
%N A378912 Irregular triangle read by rows: row n lists all positive m such that sigma(m) divides n, where sigma is the sum-of-divisors function (A000203).
%H A378912 Paolo Xausa, <a href="/A378912/b378912.txt">Table of n, a(n) for n = 1..10634</a> (rows 1..2000 of triangle, flattened).
%H A378912 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A378912 T(n,k) <= n (see A319068).
%e A378912 Triangle begins:
%e A378912   n\k|  1   2   3   4   5   6 ...
%e A378912   -------------------------------
%e A378912    1 |  1;
%e A378912    2 |  1;
%e A378912    3 |  1,  2;
%e A378912    4 |  1,  3;
%e A378912    5 |  1;
%e A378912    6 |  1,  2,  5;
%e A378912    7 |  1,  4;
%e A378912    8 |  1,  3,  7;
%e A378912    9 |  1,  2;
%e A378912   10 |  1;
%e A378912   11 |  1;
%e A378912   12 |  1,  2,  3,  5,  6, 11;
%e A378912   13 |  1,  9;
%e A378912   14 |  1,  4, 13;
%e A378912   15 |  1,  2,  8;
%e A378912   16 |  1,  3,  7;
%e A378912   17 |  1;
%e A378912   18 |  1,  2,  5, 10, 17;
%e A378912   19 |  1;
%e A378912   20 |  1,  3, 19;
%e A378912   ...
%t A378912 With[{nmax = 50}, Table[PositionIndex[Divisible[n, #[[;; n]]]][True], {n, nmax}] & [DivisorSigma[1, Range[nmax]]]]
%o A378912 (PARI) row(n) = select(x->(!(n % sigma(x))), [1..n]); \\ _Michel Marcus_, Dec 11 2024
%Y A378912 Cf. A074754 (row lengths), A319068 (right border), A378913 (row sums).
%Y A378912 Cf. A000203.
%K A378912 nonn,tabf
%O A378912 1,4
%A A378912 _Paolo Xausa_, Dec 10 2024