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A344196
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Numbers that are the sum of six fifth powers in ten or more ways.
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5
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55302546200, 89999127392, 96110537743, 104484239200, 120492759200, 121258798144, 127794946400, 133364991375, 135030535200, 136156575744, 151305014432, 155434423925, 174388570400, 177099008000, 179272687000, 180336745600, 182844944832, 184948721056, 187873845500
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OFFSET
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1,1
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LINKS
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EXAMPLE
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89999127392 is a term because 89999127392 = 4^5 + 36^5 + 39^5 + 40^5 + 90^5 + 153^5 = 8^5 + 21^5 + 90^5 + 109^5 + 119^5 + 135^5 = 8^5 + 28^5 + 98^5 + 102^5 + 104^5 + 142^5 = 10^5 + 38^5 + 74^5 + 102^5 + 118^5 + 140^5 = 13^5 + 51^5 + 64^5 + 98^5 + 112^5 + 144^5 = 18^5 + 44^5 + 66^5 + 98^5 + 112^5 + 144^5 = 18^5 + 52^5 + 72^5 + 78^5 + 118^5 + 144^5 = 28^5 + 60^5 + 63^5 + 65^5 + 124^5 + 142^5 = 36^5 + 53^5 + 62^5 + 63^5 + 129^5 + 139^5 = 39^5 + 41^5 + 64^5 + 91^5 + 98^5 + 149^5.
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PROG
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(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 >= 10])
for x in range(len(rets)):
print(rets[x])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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