A344642 Numbers that are the sum of four fifth powers in exactly one way.

4, 35, 66, 97, 128, 246, 277, 308, 339, 488, 519, 550, 730, 761, 972, 1027, 1058, 1089, 1120, 1269, 1300, 1331, 1511, 1542, 1753, 2050, 2081, 2112, 2292, 2323, 2534, 3073, 3104, 3128, 3159, 3190, 3221, 3315, 3370, 3401, 3432, 3612, 3643, 3854, 4096, 4151, 4182, 4213, 4393, 4424, 4635, 5174, 5205, 5416, 6197, 6252

Offset: 1

Author

David Consiglio, Jr., May 25 2021

Keywords

• nonn

Comments

Differs from A003349 at term 270 because 51445 = 4^5 + 8^5 + 8^5 + 8^5 = 6^5 + 7^5 + 7^5 + 9^5

Examples

			66 is a term because 66 = 1^5 + 1^5 + 2^5 + 2^5
		

Links

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

Crossrefs

Cf. A003349, A344189, A344641, A344643, A344645.

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, 4):
    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])