A027420 -id:A027420 - cp's OEIS frontend

A241944 Row sums of triangle A027420.

1, 4, 9, 20, 33, 54, 79, 114, 153, 200, 251, 320, 395, 488, 589, 700, 815, 956, 1105, 1284, 1471, 1670, 1879, 2122, 2373, 2642, 2925, 3226, 3537, 3894, 4261, 4672, 5097, 5542, 6005, 6492, 6985, 7534, 8105, 8700, 9307, 9976, 10661, 11408, 12175, 12960, 13769

Offset: 0

Reinhard Zumkeller, May 02 2014

nonn

a(n) = sum(A027420(n,k): k = 0..n).

Haskell
```
a241944 = sum . a027420_row
```

A027384 Number of distinct products i*j with 0 <= i, j <= n.

Original entry on oeis.org

1, 2, 4, 7, 10, 15, 19, 26, 31, 37, 43, 54, 60, 73, 81, 90, 98, 115, 124, 143, 153, 165, 177, 200, 210, 226, 240, 255, 268, 297, 309, 340, 355, 373, 391, 411, 424, 461, 481, 502, 518, 559, 576, 619, 639, 660, 684, 731, 748, 779, 801, 828, 851, 904, 926, 957, 979, 1009, 1039

Offset: 0

Fred Schwab (fschwab(AT)nrao.edu)

a(n) = A027420(n,0) = A027420(n,n). - Reinhard Zumkeller, May 02 2014

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)
R. P. Brent, C. Pomerance, D. Purdum, and J. Webster, Algorithms for the multiplication table, arXiv:1908.04251 [math.NT], 2019-2021.

Equals A027424 + 1, n>0.

Cf. A027417, A027427, A027425.

import Data.List (nub)
a027384 n = length $ nub [i*j | i <- [0..n], j <- [0..n]]
-- Reinhard Zumkeller, Jan 01 2012

A027384 := proc(n)
    local L,i,j ;
    L := {};
    for i from 0 to n do
        for j from i to n do
            L := L union {i*j};
        end do:
    end do:
    nops(L);
end proc: # R. J. Mathar, May 06 2016

u = {}; Table[u = Union[u, n*Range[0, n]]; Length[u], {n, 0, 100}] (* T. D. Noe, Jan 07 2012 *)

a(n) = {my(s=Set()); for (i=0, n, s = setunion(s, Set(vector(n+1, k, i*(k-1))));); #s;} \\ Michel Marcus, Jan 01 2019

def A027384(n): return len({i*j for i in range(1,n+1) for j in range(1,i+1)})+1 # Chai Wah Wu, Oct 13 2023

For prime p, a(p) = a(p - 1) + p. - David A. Corneth, Jan 01 2019

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A241944 Row sums of triangle A027420.

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A027384 Number of distinct products i*j with 0 <= i, j <= n.

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