A386966 Numbers that can be written in exactly two different ways as s_1^x_1 + ... + s_t^x_t, with 1 < s_1 < ... < s_t and {s_1,..., s_t} = {x_1,..., x_t} for some t > 0.

545, 1407, 1492, 2409, 3370, 3605, 3718, 4516, 4523, 4684, 5441, 6348, 7346, 7737, 7865, 7922, 8122, 8538, 9046, 10010, 10037, 10298, 10458, 10554, 10651, 10891, 10953, 11047, 11653, 11853, 11986, 12025, 12449, 13621, 14078, 14098, 14535, 14970, 16138, 16449, 16705, 16905, 17401, 18149, 18161, 18509

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Alberto Zanoni, BE-numbers

A. Zanoni and M. Zanoni, Sums of bases-exponents positive integer powers, Analele ştiinţifice ale Universităţii "Ovidius" Constanţa, 34-2 (2026), 197-210.

Example

 545 = 2^6  + 3^2 + 4^4 + 6^3  = 2^7 + 3^5 + 5^3 + 7^2.
1407 = 2^10 + 3^3 + 4^4 + 10^2 = 2^7 + 3^4 + 4^5 + 5^3 + 7^2.
1492 = 2^10 + 3^5 + 5^3 + 10^2 = 2^7 + 3^6 + 4^4 + 6^2 + 7^3.

Crossrefs

Subsequence of A385969.

Cf. A385232, A385233, A385970, A386967, A386968.

Sequence in context: A382137 A159626 A020259 * A184379 A374239 A353023

Adjacent sequences: A386963 A386964 A386965 * A386967 A386968 A386969

Keyword

nonn,changed

Author

Alberto Zanoni, Aug 12 2025

Status

approved