A393032 Numbers that can be written in exactly five 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.

108, 161, 162, 164, 165, 192, 213, 228, 229, 241, 242, 246, 266, 274, 281, 288, 292, 293, 299, 309, 314, 322, 330, 351, 352, 382, 383, 397, 414, 415, 428, 432, 443, 444, 446, 458, 471, 474, 479, 484, 485, 495, 498, 502, 507, 509, 523, 524, 527, 530, 535, 544, 555, 571, 585, 603, 605

Offset

1,1

Comments

Conjecture: The sequence is finite and its last number is 2879.

Links

Table of n, a(n) for n=1..57.

Alberto Zanoni, DE-numbers.

Example

108 = 2^3 + 10^2 = 3^3 + 9^2 = 2^5 + 3^3 + 7^2 = 1^5 + 2^4 + 3^3 + 8^2
    = 1^7 + 2^6 + 3^3 + 4^2;
161 = 5^3 + 6^2 = 1^5 + 2^4 + 12^2 = 2^4 + 4^3 + 9^2 = 2^6 + 3^4 + 4^2
    = 1^6 + 2^5 + 4^3 + 8^2;
162 = 3^4 + 9^2 = 1^4 + 5^3 + 6^2 = 2^5 + 3^4 + 7^2
    = 1^7 + 2^6 + 3^4 + 4^2 = 1^5 + 2^4 + 4^3 + 9^2;
...

Crossrefs

Cf. A393024, A393025, A393026, A393027, A393028, A393029, A393030, A393031, A393033, A393034.

Sequence in context: A274118 A046294 A039601 * A330851 A245032 A208088

Adjacent sequences: A393029 A393030 A393031 * A393033 A393034 A393035

Keyword

nonn

Author

Alberto Zanoni, Jan 31 2026

Status

approved