A387100 a(n) is the least number that can be written in exactly n 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}.
4, 545, 23506, 331979, 5260225, 10630307
Offset: 1
Examples
a(5) = 5260225 via
5260225 = 2^22 + 3^8 + 4^5 + 5^2 + 7^7 + 8^3 + 22^4
= 2^21 + 3^8 + 4^10 + 7^3 + 8^7 + 10^4 + 21^2
= 2^7 + 3^14 + 4^5 + 5^8 + 6^6 + 7^3 + 8^2 + 14^4
= 2^15 + 3^10 + 4^9 + 5^5 + 6^4 + 7^6 + 9^7 + 10^3 + 15^2
= 2^11 + 3^7 + 4^10 + 5^9 + 6^8 + 7^3 + 8^5 + 9^6 + 10^4 + 11^2,
and no positive integer smaller than 5260225 can be written as such in exactly five ways.