A345122 Numbers that are the sum of three third powers in exactly ten ways.

34012224, 58995000, 71319312, 72505152, 92853216, 94118760, 95331816, 139755888, 147545280, 150506000, 157464000, 159874560, 161023680, 164186352, 171904032, 182393856, 184909824, 188224128, 189771336, 191260224, 199108125, 201342240, 202440384, 217054720

Offset: 1

Author

David Consiglio, Jr., Jun 08 2021

Keywords

• nonn

Comments

Differs from A345121 at term 3 because 69190848 = 23^3 + 107^3 + 407^3 = 23^3 + 191^3 + 395^3 = 33^3 + 271^3 + 365^3 = 35^3 + 299^3 + 347^3 = 50^3 + 137^3 + 404^3 = 89^3 + 308^3 + 338^3 = 95^3 + 178^3 + 396^3 = 107^3 + 179^3 + 395^3 = 121^3 + 149^3 + 399^3 = 152^3 + 254^3 + 365^3 = 206^3 + 215^3 + 368^3.

Examples

			34012224 is a term because 34012224 = 35^3 + 215^3 + 287^3  = 38^3 + 152^3 + 311^3  = 40^3 + 113^3 + 318^3  = 44^3 + 245^3 + 266^3  = 71^3 + 113^3 + 317^3  = 99^3 + 191^3 + 295^3  = 101^3 + 226^3 + 276^3  = 117^3 + 185^3 + 295^3  = 161^3 + 215^3 + 269^3  = 172^3 + 213^3 + 266^3.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..2238

Crossrefs

Cf. A025330, A344861, A345120, A345121, A345156.

Programs

Python

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 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 08 2021