A375008 Products m of k = 3 consecutive primes p_1..p_k, where only p_1 < m^(1/k).
105, 1001, 4199, 20677, 47027, 65231, 146969, 190747, 290177, 347261, 478661, 871933, 1009091, 1201289, 1879981, 2494633, 3127361, 3864241, 4273697, 5171489, 5605027, 6672203, 7566179, 9363547, 10681031, 11592209, 13420567, 15546187, 16965341, 18181979, 19172437
Offset: 1
Examples
105 is in the sequence since m = 3*5*7 = 105 is such that 3 is less than the cube root of 105, but both 5 and 7 exceed it. 385 is not in the sequence because m = 5*7*11 = 385 is such that both 5 and 7 are less than the cube root. 1001 is in the sequence since m = 7*11*13 = 1001 is such that 7 < 1001^(1/3), but both 11 and 13 are larger than 1001^(1/3), etc.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
k = 3; s = {1}~Join~Prime[Range[k - 1]]; Reap[Do[s = Append[Rest[s], Prime[i + k - 1]]; r = Surd[Times @@ s, k]; If[Count[s, _?(# < r &)] == 1, Sow[Times @@ s] ], {i, 120}] ][[-1, 1]]
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