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A345844
Numbers that are the sum of nine fourth powers in exactly two ways.
8
264, 279, 294, 309, 324, 339, 344, 359, 374, 389, 404, 424, 439, 454, 469, 504, 549, 564, 579, 584, 614, 629, 644, 664, 679, 694, 709, 759, 789, 804, 819, 839, 854, 869, 884, 888, 903, 918, 933, 934, 948, 949, 968, 983, 998, 1013, 1014, 1029, 1044, 1048, 1059
OFFSET
1,1
COMMENTS
Differs from A345586 at term 17 because 519 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4.
LINKS
EXAMPLE
279 is a term because 279 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.
PROG
(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, 9):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 2])
for x in range(len(rets)):
print(rets[x])
KEYWORD
nonn
AUTHOR
STATUS
approved