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A346363 Numbers that are the sum of six fifth powers in exactly eight ways. 6
2295937600, 4335900525, 6251954544, 8986552608, 13413708308, 14539246326, 15277569450, 15728636000, 16770321920, 16873011232, 17572402769, 17713454592, 17960776999, 18190647200, 19621666592, 20570070125, 20827689300, 22322555200, 23461554774, 23613244800 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence differs from A345722:
9085584992 = 24^5 + 38^5 + 42^5 + 48^5 + 54^5 + 96^5
= 21^5 + 34^5 + 38^5 + 43^5 + 74^5 + 92^5
= 8^5 + 34^5 + 38^5 + 62^5 + 68^5 + 92^5
= 18^5 + 18^5 + 44^5 + 64^5 + 66^5 + 92^5
= 13^5 + 18^5 + 51^5 + 64^5 + 64^5 + 92^5
= 8^5 + 38^5 + 41^5 + 47^5 + 79^5 + 89^5
= 5^5 + 23^5 + 29^5 + 45^5 + 85^5 + 85^5
= 8^5 + 23^5 + 41^5 + 64^5 + 82^5 + 84^5
= 12^5 + 18^5 + 38^5 + 72^5 + 78^5 + 84^5,
so 9085584992 is in A345722, but is not in this sequence.
LINKS
EXAMPLE
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,
so 2295937600 is a term.
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 == 8])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
Sequence in context: A180688 A225760 A345722 * A022240 A251490 A277720
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 14 13:28 EDT 2024. Contains 373400 sequences. (Running on oeis4.)