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

1,1

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

Links

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

Example

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

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, 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])

Crossrefs

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

Sequence in context: A266063 A282284 A003349 * A297546 A257600 A211612

Adjacent sequences: A344639 A344640 A344641 * A344643 A344644 A344645

Keyword

nonn

Author

David Consiglio, Jr., May 25 2021

Status

approved