A344641 Numbers that are the sum of three positive fifth powers in exactly one way.

3, 34, 65, 96, 245, 276, 307, 487, 518, 729, 1026, 1057, 1088, 1268, 1299, 1510, 2049, 2080, 2291, 3072, 3127, 3158, 3189, 3369, 3400, 3611, 4150, 4181, 4392, 5173, 6251, 6282, 6493, 7274, 7778, 7809, 7840, 8020, 8051, 8262, 8801, 8832, 9043, 9375, 9824, 10902, 10933, 11144, 11925, 14026, 15553, 15584, 15795

Offset: 1

Author

David Consiglio, Jr., May 25 2021

Keywords

• nonn

Comments

Differs from A003348 at term 44785 because 1375298099 = 3^5 + 54^5 + 62^5 = 24^5 + 28^5 + 67^5. [Corrected by Patrick De Geest, Dec 27 2024]

Examples

			65 is a term because 65 = 1^5 + 2^5 + 2^5.
		

Links

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

Crossrefs

Cf. A003348, A344188, A344642.

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, 3):
    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])