A344751 Numbers that are the sum of three fourth powers in exactly nine ways.

105760443698, 131801075042, 187758243218, 253590205778, 319889609522, 445600096578, 510334859762, 601395185762, 615665999858, 730871934338, 749472385298, 855952663202, 856722174098, 951843993282, 1157106866258, 1186209675378, 1290443616098, 1455023522498

Offset: 1

Author

David Consiglio, Jr., May 28 2021

Keywords

• nonn

Comments

Differs from A344750 at term 1 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.

Examples

			105760443698 is a term because 105760443698 = 7^4 + 476^4 + 483^4  = 51^4 + 452^4 + 503^4  = 76^4 + 437^4 + 513^4  = 107^4 + 417^4 + 524^4  = 133^4 + 399^4 + 532^4  = 199^4 + 348^4 + 547^4  = 212^4 + 337^4 + 549^4  = 228^4 + 323^4 + 551^4  = 252^4 + 301^4 + 553^4.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..23

Crossrefs

Cf. A344738, A344750, A344861, A344927, A345120.

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 == 9])
for x in range(len(rets)):
    print(rets[x])