A378912 - OEIS

%I #22 Dec 12 2024 15:12:28

%S 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 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 1,2,1,3,4,12,13,1,1,2,5,8,29,1,16,25,1,3,7,21,31

%N 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 Paolo Xausa, <a href="/A378912/b378912.txt">Table of n, a(n) for n = 1..10634</a> (rows 1..2000 of triangle, flattened).

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F T(n,k) <= n (see A319068).

%e Triangle begins:

%e   n\k|  1   2   3   4   5   6 ...

%e   -------------------------------

%e    1 |  1;

%e    2 |  1;

%e    3 |  1,  2;

%e    4 |  1,  3;

%e    5 |  1;

%e    6 |  1,  2,  5;

%e    7 |  1,  4;

%e    8 |  1,  3,  7;

%e    9 |  1,  2;

%e   10 |  1;

%e   11 |  1;

%e   12 |  1,  2,  3,  5,  6, 11;

%e   13 |  1,  9;

%e   14 |  1,  4, 13;

%e   15 |  1,  2,  8;

%e   16 |  1,  3,  7;

%e   17 |  1;

%e   18 |  1,  2,  5, 10, 17;

%e   19 |  1;

%e   20 |  1,  3, 19;

%e   ...

%t With[{nmax = 50}, Table[PositionIndex[Divisible[n, #[[;; n]]]][True], {n, nmax}] & [DivisorSigma[1, Range[nmax]]]]

%o (PARI) row(n) = select(x->(!(n % sigma(x))), [1..n]); \\ _Michel Marcus_, Dec 11 2024

%Y Cf. A074754 (row lengths), A319068 (right border), A378913 (row sums).

%Y Cf. A000203.

%K nonn,tabf,new

%O 1,4

%A _Paolo Xausa_, Dec 10 2024