A344862 Numbers that are the sum of three fourth powers in ten or more ways.

49511121842, 281539574498, 364765611938, 401069383442, 541692688082, 703409488418, 792177949472, 971024246738, 1067666696642, 1090123576178, 1315120863602, 1383280118402, 1442012945282, 1561211646722, 1828395925538, 1868287026242, 1872511131218, 2054230720178

Offset: 1

Author

David Consiglio, Jr., May 31 2021

Keywords

• nonn

Examples

			49511121842 is a term because 49511121842 = 13^4 + 390^4 + 403^4  = 35^4 + 378^4 + 413^4  = 70^4 + 357^4 + 427^4  = 103^4 + 335^4 + 438^4  = 117^4 + 325^4 + 442^4  = 137^4 + 310^4 + 447^4  = 175^4 + 322^4 + 441^4  = 182^4 + 273^4 + 455^4  = 202^4 + 255^4 + 457^4  = 225^4 + 233^4 + 458^4.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..21

Crossrefs

Cf. A344750, A344861, A344928, A345121.

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, 3):
    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])