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

1,1

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

Cf. A372209, A372319, A372419.

Sequence in context: A228303 A033593 A297542 * A266105 A376001 A058844

Adjacent sequences: A375005 A375006 A375007 * A375009 A375010 A375011

Keyword

nonn,easy

Author

Michael De Vlieger, Sep 11 2024

Status

approved