cp's OEIS Frontend

A381402 Numbers k such that the set P of bases and exponents in the prime factorization of k (including exponents = 1) contains all numbers from min(P) to max(P).

%I A381402 #9 Feb 25 2025 11:40:10
%S A381402 2,4,6,8,9,12,18,24,27,36,48,54,72,81,108,144,162,216,240,324,432,625,
%T A381402 648,720,810,1200,1296,1620,2000,2025,2160,2592,3125,3240,3600,3750,
%U A381402 3888,4050,5000,5625,6000,6480,7500,8100,10125,10800,11250,12960,15000,15625
%N A381402 Numbers k such that the set P of bases and exponents in the prime factorization of k (including exponents = 1) contains all numbers from min(P) to max(P).
%e A381402 48 is a term because 48 = 2^4*3^1, the set of these bases and exponents is {1, 2, 3, 4} and this set contains all numbers from 1 to 4.
%e A381402 2000 is a term because 2000 = 2^4*5^3, the set of these bases and exponents is {2, 3, 4, 5} and this set contains all numbers from 2 to 5.
%t A381402 A381402Q[k_] := Range @@ MinMax[#] == # & [Union[Flatten[FactorInteger[k]]]];
%t A381402 Select[Range[2, 20000], A381402Q]
%Y A381402 Cf. A381398.
%K A381402 nonn
%O A381402 1,1
%A A381402 _Paolo Xausa_, Feb 24 2025