A344861 Numbers that are the sum of three fourth powers in exactly ten ways.

49511121842, 364765611938, 703409488418, 792177949472, 2667500248322, 3602781562562, 3999861055442, 4010400869202, 5698033074818, 5836249791008, 6330685395762, 7250378688098, 7695882509378, 8746828790882, 10383571090802, 11254551814688, 12160605587858

Offset

1,1

Comments

Differs from A344862 at term 2 because 281539574498 = 7^4 + 609^4 + 616^4 = 41^4 + 591^4 + 632^4 = 81^4 + 568^4 + 649^4 = 99^4 + 557^4 + 656^4 = 121^4 + 543^4 + 664^4 = 168^4 + 511^4 + 679^4 = 224^4 + 469^4 + 693^4 = 239^4 + 457^4 + 696^4 = 256^4 + 443^4 + 699^4 = 269^4 + 432^4 + 701^4 = 293^4 + 411^4 + 704^4 = 336^4 + 371^4 + 707^4.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..40

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. A344751, A344862, A344929, A345122.

Sequence in context: A195283 A344750 A344862 * A179228 A084482 A216019

Adjacent sequences: A344858 A344859 A344860 * A344862 A344863 A344864

Keyword

nonn

Author

David Consiglio, Jr., May 31 2021

Extensions

More terms from Sean A. Irvine, Jun 01 2021

Status

approved