A386968 Numbers that can be written in exactly four 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.

331979, 536134, 602342, 848707, 1007017, 1360430, 1484182, 1767157, 1891086, 2024074, 2036922, 2095031, 2097159, 2231826, 2257754, 2292303, 2293830, 2320578, 2440812, 2503676, 2590739, 2744591, 2852016, 2890344, 2914526, 2944901, 2951290, 3019920, 3020295, 3053910, 3121946, 3157114, 3310022

Offset: 1

Author

Alberto Zanoni, Aug 12 2025

Keywords

• nonn

Examples

			331979 = 2^15 + 4^5  + 5^6 + 6^7 + 7^4 + 15^2
       = 2^2 + 3^8  + 4^9 + 5^3 + 8^4 + 9^5
       = 2^5  + 3^10 + 4^9 + 5^2 + 9^3 + 10^4
       = 2^6 + 3^10 + 4^9 + 5^5 + 6^2 + 9^4 + 10^3.
536134 = 2^6 + 3^12 + 4^3 + 5^5 + 6^4 + 12^2
       = 2^16 + 3^10 + 4^9 + 5^7 + 6^6 + 7^5  + 9^4
       = 2^16 + 4^8  + 5^5 + 6^7 + 7^6 + 8^4  + 16^2
       = 2^18 + 3^11 + 4^4 + 5^7 + 7^5 + 11^3 + 18^2.
602342 = 2^16 + 3^12 + 4^4 + 5^5 + 12^3 + 16^2
       = 2^8  + 3^12 + 4^3 + 5^5 + 6^6 + 8^2 + 12^4
       = 2^13 + 3^8  + 4^2 + 5^3 + 6^7 + 7^5 + 8^6 + 13^4
       = 2^15 + 3^10 + 4^8 + 5^7 + 6^4 + 7^2 + 8^6 + 10^5 + 15^3.
5260225 is not in the sequence as it can be written in exactly five ways a such. - _David A. Corneth_, Aug 16 2025
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..3353 (terms <= 10^8)

Crossrefs

Subsequence of A385969.

Cf. A385232, A385233, A385970, A386966, A386967.