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Products m of k = 4 consecutive primes p_1..p_k, where only p_1 < m^(1/k).
2

%I #4 Sep 16 2024 12:53:06

%S 257557397,490995677,1314423991,2445956099,8756100193,14406533983,

%T 34491476237,168268429891,453178561051,526847565721,588771800473,

%U 673542175381,874245022517,1129796633837,1267153039517,1385645583389,1742522070781,2638237130051,3021997659211,3389753359877

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

%C 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.

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

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

%H Michael De Vlieger, <a href="/A375975/b375975.txt">Table of n, a(n) for n = 1..65536</a>

%t 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]]

%Y Cf. A138637, A375974.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Sep 12 2024