Original entry on oeis.org
4, 8, 9, 16, 18, 24, 25, 27, 32, 36, 40, 48, 49, 50, 54, 56, 64, 72, 75, 80, 81, 88, 96, 98, 100, 104, 108, 112, 120, 121, 125, 128, 135, 136, 144, 147, 152, 160, 162, 168, 169, 176, 180, 184, 189, 192, 196, 200, 208, 216, 224, 225, 232, 240, 242, 243, 245
Offset: 1
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With[{nn = 57}, Take[#, nn] &@ Sort@ Table[SelectFirst[n + Range[7 + n^2], AnyTrue[Power[#, 1/3] & /@ {n #, n #^2}, IntegerQ] &], {n, 8 nn}]] (* Michael De Vlieger, Feb 03 2018 *)
A277780
a(n) is the least k > n such that n*k^2 is a cube.
Original entry on oeis.org
8, 16, 24, 32, 40, 48, 56, 27, 72, 80, 88, 96, 104, 112, 120, 54, 136, 144, 152, 160, 168, 176, 184, 81, 200, 208, 64, 224, 232, 240, 248, 108, 264, 272, 280, 288, 296, 304, 312, 135, 328, 336, 344, 352, 360, 368, 376, 162, 392, 400, 408, 416, 424, 128, 440
Offset: 1
a(24) = 81 because 24 * 81^2 = 54^3;
a(25) = 200 because 25 * 200^2 = 100^3;
a(26) = 208 because 26 * 208^2 = 104^3;
a(27) = 64 because 27 * 64^2 = 48^3.
The cubefree part of 144 is 18. The cubefull part of 144 is 8 = 2^3. Therefore, a(144) = 18 * 3^3 = 486. - _David A. Corneth_, Nov 01 2016
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Table[k = n + 1; While[! IntegerQ[(n k^2)^(1/3)], k++]; k, {n, 55}] (* Michael De Vlieger, Nov 04 2016 *)
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a(n) = {my(k = n+1); while (!ispower(n*k^2, 3), k++); k;} \\ Michel Marcus, Oct 31 2016
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a(n) = {my(f = factor(n)); f[, 2] = f[, 2]%3; f=factorback(f); n = sqrtnint(n/f,3); (n+1)^3 * f} \\ David A. Corneth, Nov 01 2016
A343881
Table read by antidiagonals upward: T(n,k) is the least integer m > k such that k^x * m^y = c^n for some positive integers c, x, and y where x < n and y < n; n >= 2, k >= 1.
Original entry on oeis.org
4, 8, 8, 4, 4, 12, 32, 4, 9, 9, 4, 4, 9, 16, 20, 128, 4, 9, 8, 25, 24, 4, 4, 9, 8, 20, 36, 28, 8, 4, 9, 8, 25, 24, 49, 18, 4, 4, 9, 8, 20, 36, 28, 27, 16, 2048, 4, 9, 8, 25, 24, 49, 18, 24, 40, 4, 4, 9, 8, 20, 36, 28, 16, 12, 80, 44, 8192, 4, 9, 8, 25, 24, 49
Offset: 2
Table begins:
n\k| 1 2 3 4 5 6 7 8 9 10
-----+-----------------------------------------
2 | 4, 8, 12, 9, 20, 24, 28, 18, 16, 40
3 | 8, 4, 9, 16, 25, 36, 49, 27, 24, 80
4 | 4, 4, 9, 8, 20, 24, 28, 18, 12, 40
5 | 32, 4, 9, 8, 25, 36, 49, 16, 27, 100
6 | 4, 4, 9, 8, 20, 24, 28, 9, 16, 40
7 | 128, 4, 9, 8, 25, 36, 49, 16, 27, 100
8 | 4, 4, 9, 8, 20, 24, 28, 16, 12, 40
9 | 8, 4, 9, 8, 25, 36, 49, 16, 24, 80
10 | 4, 4, 9, 8, 20, 24, 28, 16, 16, 40
11 | 2048, 4, 9, 8, 25, 36, 49, 16, 27, 100
T(2, 3) = 12 with 3 * 12 = 6^2.
T(3,10) = 80 with 10^2 * 80 = 20^3.
T(4, 5) = 20 with 5^2 * 20^2 = 10^4.
T(5, 1) = 32 with 1 * 32 = 2^5.
T(6, 8) = 9 with 8^2 * 9^3 = 6^6.
Showing 1-3 of 3 results.
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