A345600 Numbers that are the sum of ten fourth powers in seven or more ways.

4485, 5445, 5460, 5525, 5540, 5590, 5605, 5670, 5700, 5715, 5765, 5780, 5830, 5845, 6645, 6675, 6710, 6740, 6755, 6775, 6805, 6820, 6855, 6870, 6885, 6900, 6915, 6930, 6935, 6950, 6965, 6980, 6995, 7015, 7030, 7045, 7060, 7095, 7110, 7125, 7175, 7190, 7235

Offset

1,1

Links

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

Example

5445 is a term because 5445 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 4^4 + 7^4 + 7^4 = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 7^4 = 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 6^4 = 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 8^4 = 4^4 + 4^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 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, 10):
    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. A345555, A345591, A345599, A345601, A345639, A345859.

Sequence in context: A179161 A139068 A232200 * A345859 A031565 A031745

Adjacent sequences: A345597 A345598 A345599 * A345601 A345602 A345603

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved