A321491
Numbers of the form (x+y)(x^2+y^2), with integers x > y > 0.
Original entry on oeis.org
15, 40, 65, 85, 120, 156, 175, 203, 259, 272, 320, 369, 400, 405, 477, 520, 580, 585, 671, 680, 715, 803, 820, 888, 935, 960, 1080, 1105, 1111, 1157, 1248, 1261, 1400, 1417, 1464, 1484, 1624, 1625, 1695, 1755, 1820, 1875, 1885, 2055, 2072, 2080, 2176, 2295, 2336, 2380, 2465
Offset: 1
Let f(x,y) = (x+y)(x^2+y^2) = A321490(x,y), then:
a(1) = f(2,1) = 3*5 = 15,a(2) = f(3,1) = 4*10 = 40, a(3) = f(3,2) = 5*13 = 65,a(4) = f(4,1) = 5*17 = 85,a(5) = f(4,2) = 6*20 = 120, etc.
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list_A321491(L=1e4,S=[])={for(m=2, sqrtnint(L, 3), for(n=1, m-1, if(L
A321490
Triangular table T[n,k] = (n+k)(n^2+k^2), 1 <= k <= n = 1, 2, 3, ...; read by rows.
Original entry on oeis.org
4, 15, 32, 40, 65, 108, 85, 120, 175, 256, 156, 203, 272, 369, 500, 259, 320, 405, 520, 671, 864, 400, 477, 580, 715, 888, 1105, 1372, 585, 680, 803, 960, 1157, 1400, 1695, 2048, 820, 935, 1080, 1261, 1484, 1755, 2080, 2465, 2916, 1111, 1248, 1417, 1624, 1875, 2176, 2533, 2952, 3439, 4000, 1464, 1625, 1820, 2055, 2336
Offset: 1
The table starts:
Row 1: 4;
Row 2: 15, 32;
Row 3: 40, 65, 108;
Row 4: 85, 120, 175, 256;
Row 5: 156, 203, 272, 369, 500;
Row 6: 259, 320, 405, 520, 671, 864;
Row 7: 400, 477, 580, 715, 888, 1105, 1372;
Row 8: 585, 680, 803, 960, 1157, 1400, 1695, 2048;
etc.
Cf.
A321491 (numbers of the form T(n,k) with n > k > 0).
Cf.
A321492 (numbers which can be written at least twice in this form).
Cf.
A198063 (read as a square array equals T(n,k) for all n, k >= 0).
Cf.
A321500 (variant of this table with additional row 0 and column 0).
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t[n_, k_] := (n + k) (n^2 + k^2); Table[t[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Amiram Eldar, Nov 22 2018 *)
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A321490(n,k)=(n+k)*(n^2+k^2)
A321490_row(n)=vector(n,k,(n+k)*(n^2+k^2))
A321490_list(N=12)=concat(apply(A321490_row,[1..N]))
Showing 1-2 of 2 results.
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