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

1,1

Links

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

Example

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.

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, 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])

Crossrefs

Cf. A344750, A344861, A344928, A345121.

Sequence in context: A092381 A195283 A344750 * A344861 A179228 A084482

Adjacent sequences: A344859 A344860 A344861 * A344863 A344864 A344865

Keyword

nonn

Author

David Consiglio, Jr., May 31 2021

Status

approved