A214448
Least m>0 such that m^4 >= n!.
Original entry on oeis.org
1, 2, 2, 3, 4, 6, 9, 15, 25, 44, 80, 148, 281, 544, 1070, 2139, 4343, 8946, 18676, 39495, 84545, 183102, 400981, 887517, 1984548, 4481308, 10215173, 23498233, 54529901, 127618907, 301130984, 716214216
Offset: 1
a(4)=3 because 3^2 < 4! <= 3^3.
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A214448 := proc(n)
ceil(root[4](n!)) ;
end proc: # R. J. Mathar, Jul 24 2012
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Table[Ceiling[n!^(1/4)], {n, 1, 40}]
A308852
Minimum number k such that the k-th tetrahedral number is not smaller than n!.
Original entry on oeis.org
1, 2, 3, 5, 8, 16, 31, 62, 129, 279, 621, 1421, 3343, 8057, 19870, 50071, 128747, 337414, 900358, 2443947, 6742667, 18893218, 53729800, 154983562, 453174686, 1342528227, 4027584682, 12230119228, 37574801086, 116753643340, 366767636286, 1164414663338, 3734900007009
Offset: 1
The minimum tetrahedral number not smaller than 4! is 35 (i.e., the 5th tetrahedral number), so a(4) = 5.
The minimum tetrahedral number not smaller (equal, in fact) than 5! is 120 (i.e., the 8th tetrahedral number), so a(5) = 8.
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Floor[(6 Range[33]!)^(1/3)] (* Giovanni Resta, Jul 30 2019 *)
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a(n) = {my(k=1); while (k*(k+1)*(k+2)/6 < n!, k++); k;} \\ Michel Marcus, Jun 28 2019
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