A345814 Numbers that are the sum of six fourth powers in exactly two ways.

261, 276, 291, 341, 356, 421, 516, 531, 596, 771, 885, 900, 965, 1140, 1361, 1509, 1556, 1571, 1636, 1811, 2180, 2596, 2611, 2661, 2691, 2706, 2721, 2741, 2756, 2771, 2786, 2836, 2931, 2946, 2961, 3011, 3026, 3091, 3186, 3201, 3220, 3266, 3285, 3300, 3315

Offset: 1

Author

David Consiglio, Jr., Jun 26 2021

Keywords

• nonn

Comments

Differs from A345559 at term 25 because 2676 = 1^4 + 1^4 + 2^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4.

Examples

			276 is a term because 276 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.
		

Links

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

Crossrefs

Cf. A048930, A344237, A345559, A345813, A345815, A345824, A346357.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 2])
    for x in range(len(rets)):
        print(rets[x])