OFFSET
1,1
COMMENTS
In other words, products m of k = 3 consecutive primes p_1..p_k, where floor(log_p_1 m) >= k but floor(log_p_j m) = k-1, j > 1.
For m = 105, floor(log_3 105) > k but floor(log_p_j 105) = k-1 for j > 1.
For m > 105, floor(log_p_1 m) = k but floor(log_p_j m) = k-1 for j > 1.
Superset of A372419.
Does not intersect A372319.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
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]]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Sep 11 2024
STATUS
approved