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A346364 Numbers that are the sum of six fifth powers in exactly nine ways. 6
9085584992, 16933805856, 37377003050, 39254220544, 41066625600, 41485873792, 42149876800, 43828403850, 44180505600, 45902654525, 48588434400, 52005184992, 53536896864, 54156285568, 56229189632, 57088402525, 59954496800, 63432407850, 66188522400, 66507304800 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Differs from A345723 at term 15 because 55302546200 = 34^5 + 38^5 + 50^5 + 57^5 + 95^5 + 136^5 = 23^5 + 49^5 + 61^5 + 69^5 + 107^5 + 131^5 = 24^5 + 37^5 + 63^5 + 81^5 + 104^5 + 131^5 = 21^5 + 35^5 + 60^5 + 94^5 + 100^5 + 130^5 = 57^5 + 60^5 + 71^5 + 75^5 + 109^5 + 128^5 = 19^5 + 37^5 + 56^5 + 96^5 + 104^5 + 128^5 = 35^5 + 41^5 + 53^5 + 69^5 + 115^5 + 127^5 = 16^5 + 49^5 + 53^5 + 83^5 + 112^5 + 127^5 = 35^5 + 37^5 + 40^5 + 88^5 + 119^5 + 121^5 = 11^5 + 24^5 + 71^5 + 104^5 + 109^5 + 121^5.
LINKS
EXAMPLE
9085584992 is a term because 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.
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 == 9])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
Sequence in context: A345863 A346257 A345723 * A015398 A034614 A140501
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified April 23 08:33 EDT 2024. Contains 371905 sequences. (Running on oeis4.)