A345591 Numbers that are the sum of nine fourth powers in seven or more ways.

6739, 6804, 6854, 6869, 6979, 7029, 7044, 7094, 7109, 7269, 7284, 7844, 7909, 7939, 8004, 8019, 8084, 8149, 8194, 8244, 8259, 8309, 8324, 8389, 8434, 8499, 8564, 8628, 8739, 8868, 8979, 9044, 9059, 9124, 9189, 9219, 9234, 9254, 9284, 9299, 9364, 9414, 9429

Offset

1,1

Links

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

Example

6804 is a term because 6804 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 = 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 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, 9):
    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

Cf. A345546, A345582, A345590, A345592, A345600, A345624, A345849.

Sequence in context: A249463 A031642 A257486 * A345849 A253230 A253349

Adjacent sequences: A345588 A345589 A345590 * A345592 A345593 A345594

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved