A345580 Numbers that are the sum of eight fourth powers in five or more ways.

4228, 4403, 4468, 5443, 5508, 5683, 6613, 6643, 6658, 6708, 6723, 6773, 6788, 6838, 6853, 6868, 6883, 6898, 6948, 6963, 7013, 7028, 7093, 7138, 7203, 7267, 7268, 7332, 7397, 7478, 7507, 7572, 7588, 7828, 7858, 7923, 7938, 7988, 8003, 8068, 8113, 8133, 8178

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Example

4403 is a term because 4403 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 8^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4.

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, 8):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 5])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A345535, A345571, A345579, A345581, A345589, A345613, A345837.

Sequence in context: A031563 A031743 A236725 * A345837 A210092 A035899

Adjacent sequences: A345577 A345578 A345579 * A345581 A345582 A345583

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved