A346278 Numbers that are the sum of seven fifth powers in exactly one way.

7, 38, 69, 100, 131, 162, 193, 224, 249, 280, 311, 342, 373, 404, 435, 491, 522, 553, 584, 615, 646, 733, 764, 795, 826, 857, 975, 1006, 1030, 1037, 1061, 1068, 1092, 1123, 1154, 1185, 1216, 1217, 1248, 1272, 1279, 1303, 1334, 1365, 1396, 1427, 1459, 1490

Offset: 1

Author

David Consiglio, Jr., Jul 13 2021

Keywords

• nonn

Comments

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.

Examples

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

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Python

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 1])
    for x in range(len(rets)):
        print(rets[x])