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A344811
Numbers that are the sum of six squares in seven or more ways.
6
60, 65, 68, 69, 77, 78, 81, 84, 86, 87, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136
OFFSET
1,1
LINKS
EXAMPLE
65 = 1^2 + 1^2 + 1^2 + 1^2 + 5^2 + 6^2
= 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 7^2
= 1^2 + 1^2 + 2^2 + 3^2 + 5^2 + 5^2
= 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 6^2
= 1^2 + 2^2 + 2^2 + 2^2 + 4^2 + 6^2
= 2^2 + 2^2 + 3^2 + 4^2 + 4^2 + 4^2
= 2^2 + 3^2 + 3^2 + 3^2 + 3^2 + 5^2
so 65 is a term.
PROG
(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, 6):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 7])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved