A345822 Numbers that are the sum of six fourth powers in exactly ten ways.

122915, 151556, 161475, 162755, 173075, 183620, 185315, 199106, 199940, 201875, 202275, 204275, 204340, 204595, 206115, 207395, 209795, 211075, 213731, 217826, 217891, 218515, 221250, 223955, 224180, 225875, 226595, 227186, 228035, 236195, 237796, 237890

Offset

1,1

Comments

Differs from A345567 at term 8 because 197795 = 1^4 + 2^4 + 5^4 + 6^4 + 16^4 + 19^4 = 1^4 + 2^4 + 7^4 + 11^4 + 12^4 + 20^4 = 1^4 + 2^4 + 10^4 + 12^4 + 17^4 + 17^4 = 2^4 + 4^4 + 7^4 + 9^4 + 13^4 + 20^4 = 2^4 + 11^4 + 13^4 + 14^4 + 15^4 + 16^4 = 3^4 + 6^4 + 6^4 + 9^4 + 13^4 + 20^4 = 3^4 + 6^4 + 7^4 + 14^4 + 15^4 + 18^4 = 4^4 + 9^4 + 11^4 + 12^4 + 15^4 + 18^4 = 7^4 + 7^4 + 14^4 + 14^4 + 15^4 + 16^4.

Links

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

Example

151556 is a term because 151556 = 1^4 + 2^4 + 2^4 + 9^4 + 11^4 + 19^4 = 1^4 + 2^4 + 3^4 + 7^4 + 16^4 + 17^4 = 1^4 + 8^4 + 11^4 + 12^4 + 13^4 + 17^4 = 2^4 + 3^4 + 7^4 + 8^4 + 11^4 + 19^4 = 3^4 + 3^4 + 3^4 + 4^4 + 12^4 + 19^4 = 3^4 + 4^4 + 11^4 + 11^4 + 14^4 + 17^4 = 3^4 + 4^4 + 13^4 + 13^4 + 13^4 + 16^4 = 4^4 + 6^4 + 9^4 + 9^4 + 9^4 + 19^4 = 4^4 + 7^4 + 11^4 + 11^4 + 11^4 + 18^4 = 4^4 + 8^4 + 9^4 + 13^4 + 13^4 + 17^4.

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 == 10])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A341898, A345567, A345772, A345821, A345832, A346365.

Sequence in context: A115545 A224584 A345567 * A254017 A254024 A254891

Adjacent sequences: A345819 A345820 A345821 * A345823 A345824 A345825

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved