A346278 - OEIS

%I #9 Jul 31 2021 19:11:45

%S 7,38,69,100,131,162,193,224,249,280,311,342,373,404,435,491,522,553,

%T 584,615,646,733,764,795,826,857,975,1006,1030,1037,1061,1068,1092,

%U 1123,1154,1185,1216,1217,1248,1272,1279,1303,1334,1365,1396,1427,1459,1490

%N Numbers that are the sum of seven fifth powers in exactly one way.

%C Differs from A003352 at term 123 because 4099 = 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.

%H Sean A. Irvine, <a href="/A346278/b346278.txt">Table of n, a(n) for n = 1..10000</a>

%e 7 is a term because 7 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5.

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**5 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 7):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v == 1])

%o     for x in range(len(rets)):

%o         print(rets[x])

%Y Cf. A003352, A345823, A346279, A346326, A346356.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jul 13 2021