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A346362
Numbers that are the sum of six fifth powers in exactly seven ways.
6
1184966816, 1700336000, 1717860100, 1972000800, 2229475325, 2396275200, 2548597632, 2625460992, 2886251808, 3217068800, 3697267200, 3729261536, 3765398725, 4046532448, 4165116967, 4246566632, 4286704224, 4489548050, 4539955200, 4623694108, 4710031469
OFFSET
1,1
COMMENTS
Differs from A345721 at term 6 because 2295937600 = 4^5 + 21^5 + 38^5 + 42^5 + 43^5 + 72^5 = 8^5 + 16^5 + 30^5 + 42^5 + 54^5 + 70^5 = 8^5 + 13^5 + 36^5 + 37^5 + 57^5 + 69^5 = 14^5 + 16^5 + 16^5 + 52^5 + 54^5 + 68^5 = 3^5 + 14^5 + 32^5 + 44^5 + 61^5 + 66^5 = 4^5 + 18^5 + 22^5 + 52^5 + 58^5 + 66^5 = 10^5 + 14^5 + 26^5 + 42^5 + 63^5 + 65^5 = 1^5 + 7^5 + 34^5 + 57^5 + 58^5 + 63^5.
LINKS
EXAMPLE
1184966816 is a term because 1184966816 = 15^5 + 24^5 + 27^5 + 38^5 + 39^5 + 63^5 = 2^5 + 28^5 + 36^5 + 36^5 + 42^5 + 62^5 = 4^5 + 24^5 + 38^5 + 38^5 + 40^5 + 62^5 = 21^5 + 32^5 + 37^5 + 41^5 + 45^5 + 60^5 = 8^5 + 14^5 + 34^5 + 40^5 + 52^5 + 58^5 = 11^5 + 17^5 + 22^5 + 49^5 + 51^5 + 56^5 = 11^5 + 16^5 + 22^5 + 52^5 + 52^5 + 53^5.
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, 6):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 7])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved