A344750 Numbers that are the sum of three fourth powers in nine or more ways.

49511121842, 105760443698, 131801075042, 187758243218, 253590205778, 281539574498, 319889609522, 364765611938, 401069383442, 445600096578, 510334859762, 541692688082, 601395185762, 615665999858, 703409488418, 730871934338, 749472385298, 792177949472

Offset

1,1

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..41

Example

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.

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

Crossrefs

Cf. A344737, A344751, A344862, A344926, A345119.

Sequence in context: A003933 A092381 A195283 * A344862 A344861 A179228

Adjacent sequences: A344747 A344748 A344749 * A344751 A344752 A344753

Keyword

nonn

Author

David Consiglio, Jr., May 28 2021

Status

approved