A391195 Integers which can be expressed as the sum of two distinct perfect powers.

5, 9, 10, 12, 13, 17, 20, 24, 25, 26, 28, 29, 31, 33, 34, 35, 36, 37, 40, 41, 43, 44, 45, 48, 50, 52, 53, 57, 58, 59, 61, 63, 65, 68, 72, 73, 74, 76, 80, 81, 82, 85, 89, 90, 91, 96, 97, 100, 101, 104, 106, 108, 109, 113, 116, 117, 122, 125, 126, 127, 129

Offset

1,1

Comments

The first integer which can be represented in two ways is 17 and the first in three ways is 129.

Links

Table of n, a(n) for n=1..61.

Example

12 = 2^2+2^3.
17 = 1+2^4 = 2^3+3^2.
129 = 1+2^7 = 2^2+5^3 = 2^3+11^2.

Mathematica

With[{m = 130}, Select[Range[m], Count[IntegerPartitions[#, {2}, Select[Range[m], # == 1 || GCD @@ FactorInteger[#][[;; , 2]] > 1 &]], _?(UnsameQ @@ #1 &)] > 0 &]] (* Amiram Eldar, Dec 04 2025 *)

Crossrefs

Cf. A000404, A001597, A388076.

Sequence in context: A139456 A195684 A135980 * A314579 A373841 A070873

Adjacent sequences: A391192 A391193 A391194 * A391196 A391197 A391198

Keyword

nonn,easy

Author

Paul Duckett, Dec 02 2025

Status

approved