A345535 Numbers that are the sum of eight cubes in five or more ways.

471, 497, 504, 597, 623, 628, 630, 635, 642, 649, 654, 661, 667, 680, 686, 691, 693, 712, 717, 719, 723, 728, 736, 738, 741, 743, 752, 754, 755, 762, 769, 774, 776, 778, 780, 781, 783, 784, 785, 788, 791, 793, 795, 797, 800, 802, 804, 810, 813, 814, 815, 817

Offset

1,1

Links

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

Example

497 is a term because 497 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 5^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 5^3 + 5^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 6^3 = 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 5^3.

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, 8):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 5])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A345492, A345523, A345534, A345536, A345544, A345580, A345787.

Sequence in context: A254416 A251771 A251152 * A345787 A265137 A265138

Adjacent sequences: A345532 A345533 A345534 * A345536 A345537 A345538

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved