A344641 Numbers that are the sum of three 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

1,1

Comments

Differs from A003348 at term 44785 because 1375298099 = 3^5 + 55^5 + 63^5 = 25^5 + 29^5 + 68^5

Links

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

Example

65 is a term because 65 = 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, 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])

Crossrefs

Cf. A003348, A344188, A344642.

Sequence in context: A110070 A074692 A003348 * A086488 A195021 A344429

Adjacent sequences: A344638 A344639 A344640 * A344642 A344643 A344644

Keyword

nonn

Author

David Consiglio, Jr., May 25 2021

Status

approved