A345579 Numbers that are the sum of eight fourth powers in four or more ways.

2933, 2948, 3013, 3173, 3188, 3557, 4148, 4163, 4213, 4228, 4293, 4388, 4403, 4453, 4468, 4643, 4772, 4837, 4883, 5012, 5123, 5188, 5203, 5268, 5333, 5363, 5378, 5398, 5428, 5443, 5508, 5538, 5573, 5603, 5618, 5668, 5683, 5733, 5748, 5858, 5923, 6052, 6163

Offset

1,1

Links

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

Example

2948 is a term because 2948 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 4^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4 = 2^4 + 2^4 + 3^4 + 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, 8):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 4])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A345534, A345570, A345578, A345580, A345588, A345612, A345836.

Sequence in context: A345570 A345826 A236648 * A345836 A345598 A345857

Adjacent sequences: A345576 A345577 A345578 * A345580 A345581 A345582

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved