A358435 -id:A358435 - cp's OEIS frontend

A357498 Triangle read by rows where each term in row n is the next greater multiple of n..1 divided by n..1.

1, 1, 3, 1, 2, 5, 1, 2, 4, 9, 1, 2, 3, 5, 11, 1, 2, 3, 5, 8, 17, 1, 2, 3, 4, 6, 10, 21, 1, 2, 3, 4, 6, 9, 14, 29, 1, 2, 3, 4, 5, 7, 10, 16, 33, 1, 2, 3, 4, 5, 7, 9, 13, 20, 41, 1, 2, 3, 4, 5, 6, 8, 11, 15, 23, 47, 1, 2, 3, 4, 5, 6, 8, 10, 13, 18, 28, 57

Offset: 1

Tamas Sandor Nagy, Oct 01 2022

This triangle is related to A357431. Terms there are divisible by n..1 and here that division is performed, leaving the respective multiple of each.
Row n has length n and columns are numbered k = 1..n corresponding to multiples n..1.
Row n begins with n/n = 1. The end-most terms of the rows are A007952.

			Triangle begins:
  n/k|  1   2   3   4   5   6   7
  --------------------------------
  1  |  1;
  2  |  1,  3;
  3  |  1,  2,  5;
  4  |  1,  2,  4,  9;
  5  |  1,  2,  3,  5, 11;
  6  |  1,  2,  3,  5,  8, 17;
  7  |  1,  2,  3,  4,  6, 10, 21;
  ...
For row n=6, we have:
  A357431 row  6 10 12 15 16 17
  divided by   6  5  4  3  2  1
  results in   1  2  3  5  8 17

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10011 (141 rows, flattened)

Cf. A358435 (row sums), A357431, A007952 (right diagonal).

row[n_] := Module[{k = n, s = Table[0, n], r}, s[[1]] = 1; Do[k++; k += If[(r = Mod[k, i]) == 0, 0, i - Mod[k, i]]; s[[n + 1 - i]] = k/i, {i, n - 1, 1, -1}]; s]; Array[row, 12] // Flatten (* Amiram Eldar, Oct 01 2022 *)

row(n) = my(v=vector(n)); v[1] = n; for (k=2, n, v[k] = v[k-1] + (n-k+1) - (v[k-1] % (n-k+1));); vector(n, k, v[k]/(n-k+1)); \\ Michel Marcus, Nov 16 2022

T(n,k) = A357431(n,k) / (n-k+1).
T(n,1) = 1.
T(n,k) = (T(n,k-1)*(n-k+2) + (n-k+1) - (T(n,k-1)*(n-k+2)) mod (n-k+1))/(n-k+1), for k >= 2.
T(n,n) = A007952(n).

cp's OEIS Frontend

A357498 Triangle read by rows where each term in row n is the next greater multiple of n..1 divided by n..1.

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