A173395 -id:A173395 - cp's OEIS frontend

A355170 The composite numbers in order of appearance in A173395.

4, 6, 8, 9, 10, 12, 15, 16, 14, 18, 20, 21, 24, 25, 28, 30, 27, 32, 35, 36, 22, 40, 42, 33, 45, 48, 49, 26, 44, 50, 54, 56, 39, 55, 60, 63, 64, 52, 66, 70, 72, 65, 77, 80, 81, 34, 78, 84, 88, 90, 51, 75, 91, 96, 99, 100, 38, 68, 98, 104, 108, 110, 57, 85, 105

Offset: 1

Denver Massey, Jun 22 2022

This sequence can be generated by removing duplicates from A173395. As such, every number in this sequence is composite, and every composite number appears in this sequence.

This gives a method of enumerating the composite numbers.

			This sequence can be generated by reading along the diagonals of the multiplication table with headers starting at 2, skipping any number that has already been seen:
   4  6  8 10 12 ...
   6  9 12 15 18 ...
   8 12 16 20 24 ...
  10 15 20 25 30 ...
  12 18 24 30 36 ...
  ...

Cf. A173395, A257471 (similar construction).

A342385 Triangle T(n,k) read by rows (n >= 0, 0 <= k <= n): first column is A001477 and column k > 0 is k*A028310.

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 3, 2, 2, 3, 4, 3, 4, 3, 4, 5, 4, 6, 6, 4, 5, 6, 5, 8, 9, 8, 5, 6, 7, 6, 10, 12, 12, 10, 6, 7, 8, 7, 12, 15, 16, 15, 12, 7, 8, 9, 8, 14, 18, 20, 20, 18, 14, 8, 9, 10, 9, 16, 21, 24, 25, 24, 21, 16, 9, 10, 11, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 11

Offset: 0

Paul Curtz, Mar 10 2021

Row sums: A177787(n) with A177787(0) = 0.
First subtriangle: A003991(n+1).
Second subtriangle: A173395(n+1).
A000290(n) is a subsequence via (2*n+1)-th rows.

			Triangle begins:
  n\k|  0   1   2   3   4   5   6   7   8   9 ...
  ---+-------------------------------------------
   0 |  0;
   1 |  1,  1;
   2 |  2,  1,  2;
   3 |  3,  2,  2,  3;
   4 |  4,  3,  4,  3,  4;
   5 |  5,  4,  6,  6,  4,  5;
   6 |  6,  5,  8,  9,  8,  5,  6;
   7 |  7,  6, 10, 12, 12, 10,  6,  7;
   8 |  8,  7, 12, 15, 16, 15, 12,  7,  8;
   9 |  9,  8, 14, 18, 20, 20, 18, 14,  8,  9;
  ...

Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of the triangle, flattened)

Cf. A000290, A001477, A003991, A028310, A173395, A177787.

With[{rowmax=10},Table[If[0Paolo Xausa, Nov 15 2023 *)

From Paolo Xausa, Nov 15 2023: (Start)
T(n,0) = T(n,n) = n.
T(n,k) = k*(n-k), for 0 < k < n. (End)

Name edited by Paolo Xausa, Nov 15 2023

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A355170 The composite numbers in order of appearance in A173395.

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A342385 Triangle T(n,k) read by rows (n >= 0, 0 <= k <= n): first column is A001477 and column k > 0 is k*A028310.

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