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A345615
Numbers that are the sum of eight fifth powers in seven or more ways.
7
4104553, 4915506, 6011150, 6027989, 6323394, 6563733, 6622231, 6776363, 6785394, 7982834, 8181481, 8288806, 8625619, 8658144, 8710484, 8742208, 8773477, 8932244, 8996669, 9252219, 9253706, 9311478, 9773236, 9904983, 9976120, 10036233, 10045233, 10053008
OFFSET
1,1
LINKS
EXAMPLE
4915506 is a term because 4915506 = 1^5 + 3^5 + 5^5 + 5^5 + 8^5 + 8^5 + 15^5 + 21^5 = 1^5 + 8^5 + 12^5 + 12^5 + 14^5 + 14^5 + 17^5 + 18^5 = 1^5 + 9^5 + 9^5 + 13^5 + 14^5 + 16^5 + 17^5 + 17^5 = 2^5 + 4^5 + 4^5 + 5^5 + 6^5 + 9^5 + 15^5 + 21^5 = 4^5 + 8^5 + 8^5 + 14^5 + 14^5 + 14^5 + 15^5 + 19^5 = 4^5 + 8^5 + 10^5 + 12^5 + 12^5 + 15^5 + 16^5 + 19^5 = 9^5 + 9^5 + 10^5 + 10^5 + 10^5 + 12^5 + 16^5 + 20^5.
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, 8):
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