A375975 Products m of k = 4 consecutive primes p_1..p_k, where only p_1 < m^(1/k).

257557397, 490995677, 1314423991, 2445956099, 8756100193, 14406533983, 34491476237, 168268429891, 453178561051, 526847565721, 588771800473, 673542175381, 874245022517, 1129796633837, 1267153039517, 1385645583389, 1742522070781, 2638237130051, 3021997659211, 3389753359877

Offset

1,1

Comments

In other words, products m of k = 4 consecutive primes p_1..p_k, where floor(log_p_1 m) >= k but floor(log_p_j m) = k-1, j > 1.

a(n) = m is such that floor(log_p_1 m) = k but floor(log_p_j m) = k-1 for j > 1.

Does not intersect A138637, since for m in A138637, both p_1 and p_2 are smaller than m^(1/k).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..65536

Mathematica

k = 4; 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. A138637, A375974.

Sequence in context: A204415 A246224 A205934 * A231202 A226448 A250433

Adjacent sequences: A375972 A375973 A375974 * A375976 A375977 A375978

Keyword

nonn

Author

Michael De Vlieger, Sep 12 2024

Status

approved