A344643 Numbers that are the sum of five positive fifth powers in exactly one way.

5, 36, 67, 98, 129, 160, 247, 278, 309, 340, 371, 489, 520, 551, 582, 731, 762, 793, 973, 1004, 1028, 1059, 1090, 1121, 1152, 1215, 1270, 1301, 1332, 1363, 1512, 1543, 1574, 1754, 1785, 1996, 2051, 2082, 2113, 2144, 2293, 2324, 2355, 2535, 2566, 2777, 3074, 3105, 3129, 3136, 3160, 3191, 3222, 3253, 3316, 3347, 3371, 3402, 3433, 3464, 3558, 3613, 3644, 3675, 3855, 3886, 4128

Offset: 1

Author

David Consiglio, Jr., May 25 2021

Keywords

• nonn

Comments

Differs from A003350 at term 67 because 4097 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 = 3^5 + 3^5 + 3^5 + 3^5 + 5^5.

Examples

			67 is a term because 67 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A003350, A342686, A344190, A344642, 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, 500)]
for pos in cwr(power_terms, 5):
    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])

Extensions

Name clarified by Patrick De Geest, Dec 24 2024