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

1,1

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.

Links

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

Example

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

Prog

(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])

Crossrefs

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

Sequence in context: A220852 A290176 A003352 * A165495 A369355 A034858

Adjacent sequences: A346275 A346276 A346277 * A346279 A346280 A346281

Keyword

nonn

Author

David Consiglio, Jr., Jul 13 2021

Status

approved