A385233 - OEIS

A385233

Numbers that can be written as s^x + t^y + u^z with 1 < s < t < u and {s,t,u} = {x,y,z} (the sequence of exponents can be any permutation of s,t,u).

%I #37 Jul 12 2026 03:46:22

%S 59,84,89,105,127,149,166,204,273,276,287,289,313,347,356,372,433,480,

%T 576,620,624,673,773,777,849,932,949,1065,1151,1201,1230,1250,1376,

%U 1380,1653,1676,2033,2089,2196,2244,2425,2534,2545,2786,3142,3156,3157,3225,3270,3302,3385,3388,3408,3445,3718,4070,4148,4249

%N Numbers that can be written as s^x + t^y + u^z with 1 < s < t < u and {s,t,u} = {x,y,z} (the sequence of exponents can be any permutation of s,t,u).

%H David A. Corneth, <a href="/A385233/b385233.txt">Table of n, a(n) for n = 1..10000</a>

%H Alberto Zanoni, <a href="https://be-numbers.jimdosite.com">BE-numbers</a>

%H A. Zanoni and M. Zanoni, <a href="https://www.anstuocmath.ro/mathematics/anale2026v2/10_ZanoniAlberto_et_all.pdf">Sums of bases-exponents positive integer powers</a>, Analele ştiinţifice ale Universităţii "Ovidius" Constanţa, 34-2 (2026), 197-210.

%e a(1) = 2^4 + 3^3 + 4^2 = 16 + 27 + 16 = 59.

%e a(2) = 2^5 + 3^3 + 5^2 = 32 + 27 + 25 = 84.

%e a(3) = 2^4 + 3^2 + 4^3 = 16 + 9 + 64 = 89.

%e a(4) = 2^3 + 3^4 + 4^2 = 8 + 81 + 16 = 105.

%Y Cf. A001597, A385232 (two addends).

%K nonn,changed

%O 1,1

%A _Alberto Zanoni_, Jun 28 2025