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).

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

Offset

1,4

Links

Paolo Xausa, Table of n, a(n) for n = 1..10634 (rows 1..2000 of triangle, flattened).

Index entries for sequences related to sigma(n)

Formula

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

Example

Triangle begins:
  n\k|  1   2   3   4   5   6 ...
  -------------------------------
   1 |  1;
   2 |  1;
   3 |  1,  2;
   4 |  1,  3;
   5 |  1;
   6 |  1,  2,  5;
   7 |  1,  4;
   8 |  1,  3,  7;
   9 |  1,  2;
  10 |  1;
  11 |  1;
  12 |  1,  2,  3,  5,  6, 11;
  13 |  1,  9;
  14 |  1,  4, 13;
  15 |  1,  2,  8;
  16 |  1,  3,  7;
  17 |  1;
  18 |  1,  2,  5, 10, 17;
  19 |  1;
  20 |  1,  3, 19;
  ...

Mathematica

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

Prog

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

Crossrefs

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

Cf. A000203.

Sequence in context: A296085 A353644 A007740 * A117811 A349431 A297381

Adjacent sequences: A378909 A378910 A378911 * A378913 A378914 A378915

Keyword

nonn,tabf,new

Author

Paolo Xausa, Dec 10 2024

Status

approved