A345853 Numbers that are the sum of ten fourth powers in exactly one ways.

10, 25, 40, 55, 70, 85, 90, 100, 105, 115, 120, 130, 135, 145, 150, 160, 165, 170, 180, 185, 195, 200, 210, 215, 225, 230, 245, 250, 260, 275, 290, 330, 370, 385, 400, 410, 435, 450, 465, 490, 500, 515, 530, 570, 610, 625, 634, 640, 649, 650, 664, 675, 679

Offset

1,1

Comments

Differs from A003344 at term 30 because 265 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4.

Links

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

Example

25 is a term because 25 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4.

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 == 1])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A003344, A345803, A345843, A345854, A346346.

Sequence in context: A198377 A038350 A003344 * A047721 A155576 A269457

Adjacent sequences: A345850 A345851 A345852 * A345854 A345855 A345856

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved