A393029 Numbers that can be written in exactly two ways as s_1^x_1 + ... + s_t^x_t, with 0 < s_1 < ... < s_t and x_1 > ... > x_t > 1 for some t > 0, with the restriction that if s_1 = 1 then x_1 is the least possible.

9, 16, 26, 32, 41, 42, 43, 49, 52, 53, 57, 58, 59, 60, 68, 69, 73, 76, 91, 98, 106, 121, 122, 124, 125, 127, 132, 133, 137, 140, 149, 155, 156, 163, 189, 201, 208, 214, 218, 222, 223, 224, 236, 240, 243, 254, 267, 268, 276, 279, 285, 291, 303, 311, 323, 327, 331, 336, 339, 342, 349, 350

Offset

1,1

Comments

Conjecture: The sequence is finite and its last number is 1446.

Links

Table of n, a(n) for n=1..62.

Alberto Zanoni, DE-numbers.

Example

 9 = 3^2       = 1^4 + 2^3;
16 = 2^4       = 4^2;
26 = 1^3 + 5^2 = 1^5 + 2^4 + 3^2;
...

Crossrefs

Cf. A393024, A393025, A393026, A393027, A393028, A393030, A393031, A393032, A393033, A393034.

Sequence in context: A161183 A183345 A303873 * A257496 A351435 A369642

Adjacent sequences: A393026 A393027 A393028 * A393030 A393031 A393032

Keyword

nonn

Author

Alberto Zanoni, Jan 31 2026

Status

approved