A345121 Numbers that are the sum of three third powers in ten or more ways.

34012224, 58995000, 69190848, 71319312, 72505152, 92853216, 94118760, 95331816, 119095488, 119409984, 139755888, 147545280, 150506000, 150547032, 157464000, 159874560, 161023680, 161350272, 164186352, 171904032, 175986000, 176175000, 182393856, 184909824

Offset: 1

Author

David Consiglio, Jr., Jun 08 2021

Keywords

• nonn

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..3429

Crossrefs

Cf. A025338, A344862, A345119, A345122, A345155.

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