A357498 -id:A357498 - cp's OEIS frontend

A358435 Row sums of the triangular array A357498.

1, 4, 8, 16, 22, 36, 47, 68, 81, 105, 125, 155, 169, 220, 239, 300, 326, 365, 414, 475, 500, 572, 635, 705, 734, 830, 897, 966, 1009, 1151, 1195, 1318, 1373, 1490, 1566, 1672, 1734, 1903, 1971, 2107, 2221, 2390, 2461, 2580, 2689, 2887, 2963, 3176, 3276, 3450, 3580, 3789, 3868

Offset: 1

Tamas Sandor Nagy, Nov 16 2022

nonn

The rows of the triangular array A357498 are chains of numbers that end with the positive terms of A007952.

			For row n=6, the next greater multiples are 6, 10, 12, 15, 16, and 17. These, divided by n..1 result in 1, 2, 3, 5, 8, and 17, the sum of which is a(6) = 36.

Cf. A357498, A007952.

a[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}]; Total[s]]; Array[a, 50] (* Amiram Eldar, Nov 16 2022 *)

a(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));); vecsum(vector(n, k, v[k]/(n-k+1))); \\ Michel Marcus, Nov 16 2022

More terms from Thomas Scheuerle, Nov 16 2022

A357431 Triangle read by rows where each term in row n is the next greater multiple of n..1.

Original entry on oeis.org

1, 2, 3, 3, 4, 5, 4, 6, 8, 9, 5, 8, 9, 10, 11, 6, 10, 12, 15, 16, 17, 7, 12, 15, 16, 18, 20, 21, 8, 14, 18, 20, 24, 27, 28, 29, 9, 16, 21, 24, 25, 28, 30, 32, 33, 10, 18, 24, 28, 30, 35, 36, 39, 40, 41, 11, 20, 27, 32, 35, 36, 40, 44, 45, 46, 47

Offset: 1

Tamas Sandor Nagy, Sep 28 2022

Row n has length n and columns are numbered k = 1..n.
Row n begins with n which is trivially divisible by n. This is followed by the least number greater than n that is divisible by n-1. Next comes the least number that is greater than this preceding one and is divisible by n-2. Then it continues the same way until the last one is reached, which is trivially divisible by 1.
The end-most terms of the rows are A007952.

			Triangle begins:
  n/k|  1   2   3   4   5   6   7
  --------------------------------
  1  |  1;
  2  |  2,  3;
  3  |  3,  4,  5;
  4  |  4,  6,  8,  9;
  5  |  5,  8,  9, 10, 11;
  6  |  6, 10, 12, 15, 16, 17;
  7  |  7, 12, 15, 16, 18, 20, 21;
  ...
For row n=6, the numbers of the chain, and below them their divisors are:
  6 10 12 15 16 17
  6  5  4  3  2  1

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..9870 (first 140 rows flattened)

Cf. A357417 (row sums), A357498, A007952 (right diagonal).

row[n_] := Module[{k = n, s = Table[0, n], r}, s[[1]] = n;Do[k++; k += If[(r = Mod[k, i]) == 0, 0, i - Mod[k, i]]; s[[n+1-i]] = k, {i, n - 1, 1, -1}]; s]; Array[row, 11] // Flatten (* Amiram Eldar, Sep 28 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));); v; \\ Michel Marcus, Nov 16 2022

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

cp's OEIS Frontend

A358435 Row sums of the triangular array A357498.

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