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

Author

David Consiglio, Jr., Jun 26 2021

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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])