A345557 Numbers that are the sum of ten cubes in nine or more ways.

632, 651, 658, 688, 695, 714, 721, 736, 740, 745, 752, 754, 756, 771, 773, 778, 780, 782, 790, 792, 795, 797, 799, 801, 806, 808, 812, 813, 815, 816, 818, 819, 821, 823, 825, 832, 834, 841, 843, 845, 847, 848, 849, 850, 851, 852, 853, 855, 856, 857, 858, 860

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Example

651 is a term because 651 = 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 5^3 + 6^3 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 7^3 = 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 5^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 5^3 + 5^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 + 4^3 + 4^3 + 5^3 = 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 6^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 4^3 + 5^3 + 5^3 = 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3.

Prog

(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, 10):
    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. A345548, A345556, A345558, A345602, A345811.

Sequence in context: A002227 A251217 A139066 * A345811 A186898 A006913

Adjacent sequences: A345554 A345555 A345556 * A345558 A345559 A345560

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved