A345560 Numbers that are the sum of six fourth powers in three or more ways.

2676, 2851, 2916, 4131, 4226, 4241, 4306, 4371, 4481, 4850, 5346, 5411, 5521, 5586, 5651, 6561, 6611, 6626, 6691, 6756, 6771, 6801, 6821, 6836, 6851, 6866, 6931, 7106, 7235, 7475, 7491, 7666, 7841, 7906, 7971, 8146, 8211, 8321, 8386, 8451, 8531, 8706, 9011

Offset

1,1

Links

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

Example

2851 is a term because 2851 = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 3])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A344243, A345512, A345559, A345561, A345569, A345604, A345815.

Sequence in context: A085559 A123075 A112138 * A345815 A166513 A345569

Adjacent sequences: A345557 A345558 A345559 * A345561 A345562 A345563

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved