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A345481
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Numbers that are the sum of seven squares in four or more ways.
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6
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37, 40, 42, 45, 46, 48, 49, 50, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108
(list;
graph;
refs;
listen;
history;
text;
internal format)
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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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40 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2 + 4^2
= 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 5^2
= 1^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2
= 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2
so 40 is a term.
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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**2 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 >= 4])
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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