A346336 Numbers that are the sum of nine fifth powers in exactly one way.

9, 40, 71, 102, 133, 164, 195, 226, 251, 257, 282, 288, 313, 344, 375, 406, 437, 468, 493, 499, 524, 555, 586, 617, 648, 679, 710, 735, 766, 797, 828, 859, 890, 921, 977, 1008, 1032, 1039, 1063, 1070, 1094, 1101, 1125, 1132, 1156, 1187, 1218, 1219, 1249, 1250

Offset

1,1

Comments

Differs from A003354 at term 191 because 4101 = 1^5 + 1^5 + 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 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

9 is a term because 9 = 1^5 + 1^5 + 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, 9):
    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. A003354, A345843, A346326, A346337, A346346.

Sequence in context: A331343 A002085 A076603 * A003354 A063164 A165372

Adjacent sequences: A346333 A346334 A346335 * A346337 A346338 A346339

Keyword

nonn

Author

David Consiglio, Jr., Jul 13 2021

Status

approved