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).

2, 4, 6, 8, 9, 12, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 240, 324, 432, 625, 648, 720, 810, 1200, 1296, 1620, 2000, 2025, 2160, 2592, 3125, 3240, 3600, 3750, 3888, 4050, 5000, 5625, 6000, 6480, 7500, 8100, 10125, 10800, 11250, 12960, 15000, 15625

Offset: 1

Author

Paolo Xausa, Feb 24 2025

Keywords

• nonn

Examples

			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.
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.
		

Crossrefs

Cf. A381398.

Programs

Mathematica

A381402Q[k_] := Range @@ MinMax[#] == # & [Union[Flatten[FactorInteger[k]]]];
Select[Range[2, 20000], A381402Q]