A381215 Numbers k such that the difference between the largest and smallest element of the set of bases and exponents (including exponents = 1) in the prime factorization of k is 1.

2, 8, 9, 36, 72, 81, 108, 216, 625, 15625, 117649, 5764801, 25937424601, 3138428376721, 23298085122481, 3937376385699289, 48661191875666868481, 14063084452067724991009, 104127350297911241532841, 37589973457545958193355601, 907846434775996175406740561329

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..155

Formula

For n >= 9, a(n) = A381317(n-4).

Example

72 is a term because 72 = 2^3*3^2, the set of these bases and exponents is {2, 3} and 3 - 2 = 1.

Mathematica

Join[{2, 8, 9, 36, 72, 81, 108, 216}, Flatten[Map[#^{# - 1, # + 1} &, Prime[Range[3, 10]]]]]

Crossrefs

Positions of ones in A381214.

Cf. A036878, A081812, A104126, A381212, A381317.

Sequence in context: A369649 A181887 A221049 * A181476 A055678 A301281

Adjacent sequences: A381212 A381213 A381214 * A381216 A381217 A381218

Keyword

nonn,easy

Author

Paolo Xausa, Feb 19 2025

Status

approved