A393028 Numbers that can be written in more than one way 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, 17, 25, 26, 32, 33, 41, 42, 43, 44, 49, 52, 53, 57, 58, 59, 60, 64, 65, 68, 69, 73, 76, 80, 81, 82, 89, 90, 91, 92, 96, 97, 98, 100, 101, 106, 107, 108, 109, 113, 114, 116, 117, 121, 122, 124, 125, 127, 128, 129, 130, 132, 133, 137, 138, 140, 141, 144, 145, 146, 149, 153, 154

Offset

1,1

Comments

Every integer greater than 1543 appears in the sequence (conjectured).

Links

Table of n, a(n) for n=1..64.

Alberto Zanoni, DE-numbers.

Example

 9 = 3^2       = 1^4 + 2^3;
16 = 4^2       = 2^4;
17 = 1^3 + 4^2 = 2^3 + 3^2 = 1^5 + 2^4;
...

Crossrefs

Cf. A393024, A393025, A393026, A393027, A393029, A393030, A393031, A393032, A393033, A393034.

Sequence in context: A231977 A269563 A217570 * A274188 A335437 A034040

Adjacent sequences: A393025 A393026 A393027 * A393029 A393030 A393031

Keyword

nonn

Author

Alberto Zanoni, Jan 31 2026

Status

approved