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A345832
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Numbers that are the sum of seven fourth powers in exactly ten ways.
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7
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31251, 44547, 45827, 45892, 47667, 47971, 49572, 51092, 53316, 53476, 54531, 54596, 54756, 57411, 58276, 58660, 59781, 59811, 59827, 59861, 59876, 59892, 61076, 64581, 65876, 65891, 66356, 66596, 66676, 67716, 67876, 68131, 68322, 68772, 69171, 69667, 70116
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OFFSET
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1,1
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COMMENTS
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Differs from A345576 at term 5 because 45907 = 1^4 + 1^4 + 3^4 + 4^4 + 8^4 + 12^4 + 12^4 = 1^4 + 6^4 + 6^4 + 8^4 + 8^4 + 9^4 + 13^4 = 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 11^4 + 13^4 = 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 11^4 + 13^4 = 2^4 + 2^4 + 4^4 + 7^4 + 7^4 + 7^4 + 14^4 = 2^4 + 3^4 + 6^4 + 6^4 + 7^4 + 7^4 + 14^4 = 2^4 + 4^4 + 6^4 + 7^4 + 9^4 + 11^4 + 12^4 = 2^4 + 5^4 + 5^4 + 10^4 + 10^4 + 10^4 + 11^4 = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 9^4 + 14^4 = 3^4 + 6^4 + 6^4 + 6^4 + 9^4 + 11^4 + 12^4 = 4^4 + 7^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4.
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LINKS
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EXAMPLE
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44547 is a term because 44547 = 1^4 + 2^4 + 2^4 + 2^4 + 6^4 + 11^4 + 13^4 = 1^4 + 2^4 + 2^4 + 6^4 + 7^4 + 7^4 + 14^4 = 1^4 + 2^4 + 6^4 + 6^4 + 9^4 + 11^4 + 12^4 = 1^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4 = 2^4 + 2^4 + 8^4 + 9^4 + 9^4 + 9^4 + 12^4 = 2^4 + 4^4 + 6^4 + 6^4 + 9^4 + 9^4 + 13^4 = 2^4 + 4^4 + 7^4 + 7^4 + 8^4 + 11^4 + 12^4 = 3^4 + 3^4 + 4^4 + 4^4 + 7^4 + 12^4 + 12^4 = 3^4 + 6^4 + 6^4 + 7^4 + 8^4 + 11^4 + 12^4 = 4^4 + 4^4 + 8^4 + 8^4 + 9^4 + 11^4 + 11^4.
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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**4 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
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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