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

1,1

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.

Links

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

Example

67 is a term because 67 = 1^5 + 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, 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])

Crossrefs

Cf. A003350, A342686, A344190, A344642, A346356.

Sequence in context: A073456 A275223 A003350 * A217166 A275143 A276249

Adjacent sequences: A344640 A344641 A344642 * A344644 A344645 A344646

Keyword

nonn

Author

David Consiglio, Jr., May 25 2021

Extensions

Name clarified by Patrick De Geest, Dec 24 2024

Status

approved