A346326 Numbers that are the sum of eight fifth powers in exactly one way.

8, 39, 70, 101, 132, 163, 194, 225, 250, 256, 281, 312, 343, 374, 405, 436, 467, 492, 523, 554, 585, 616, 647, 678, 734, 765, 796, 827, 858, 889, 976, 1007, 1031, 1038, 1062, 1069, 1093, 1100, 1124, 1155, 1186, 1217, 1218, 1248, 1249, 1273, 1280, 1304, 1311

Offset: 1

Author

David Consiglio, Jr., Jul 13 2021

Keywords

• nonn

Comments

Differs from A003353 at term 156 because 4100 = 1^5 + 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.

Examples

			8 is a term because 8 = 1^5 + 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. A003353, A345833, A346278, A346327, A346336.

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, 8):
    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])