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A346346
Numbers that are the sum of ten fifth powers in exactly one way.
5
10, 41, 72, 103, 134, 165, 196, 227, 252, 258, 283, 289, 314, 320, 345, 376, 407, 438, 469, 494, 500, 525, 531, 556, 587, 618, 649, 680, 711, 736, 742, 767, 798, 829, 860, 891, 922, 953, 978, 1009, 1033, 1040, 1064, 1071, 1095, 1102, 1126, 1133, 1157, 1164
OFFSET
1,1
COMMENTS
Differs from A003355 at term 229 because 4102 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.
LINKS
EXAMPLE
10 is a term because 10 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5.
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, 1000)]
for pos in cwr(power_terms, 10):
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
KEYWORD
nonn
AUTHOR
STATUS
approved