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

Author

David Consiglio, Jr., May 31 2021

Keywords

• nonn

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.

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

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

Crossrefs

Cf. A344751, A344862, A344929, A345122.

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])

Extensions

More terms from Sean A. Irvine, Jun 01 2021