A344035 Numbers that are the sum of five positive cubes in exactly four ways.

1252, 1376, 1461, 1522, 1548, 1585, 1590, 1646, 1702, 1709, 1737, 1739, 1772, 1798, 1802, 1810, 1864, 1889, 1954, 1987, 2006, 2033, 2081, 2096, 2152, 2160, 2225, 2241, 2251, 2276, 2313, 2322, 2339, 2341, 2367, 2374, 2377, 2416, 2423, 2456, 2458, 2465, 2467, 2512, 2521, 2528, 2530, 2537, 2540, 2549, 2556, 2582

Offset

1,1

Comments

Differs from A344034 at term 13 because 1765 = 1^3 + 1^3 + 2^3 + 3^3 + 12^3 = 1^3 + 1^3 + 6^3 + 6^3 + 11^3 = 1^3 + 2^3 + 3^3 + 9^3 + 10^3 = 3^3 + 4^3 + 6^3 + 9^3 + 9^3 = 4^3 + 4^3 + 5^3 + 8^3 + 10^3

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Example

1461 is a member of this sequence because 1461 = 1^3 + 1^3 + 1^3 + 9^3 + 9^3 = 1^3 + 1^3 + 4^3 + 4^3 + 11^3 = 3^3 + 3^3 + 4^3 + 7^3 + 10^3 = 6^3 + 6^3 + 7^3 + 7^3 + 7^3

Mathematica

s5pcQ[n_]:=Length[Select[PowersRepresentations[n, 5, 3], FreeQ[#, 0]&]]==4; Select[Range[ 3000], s5pcQ] (* Harvey P. Dale, Sep 15 2024 *)

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, 50)]
for pos in cwr(power_terms, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 4])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A294738, A343705, A343972, A343988, A344034, A344355, A345766.

Sequence in context: A186477 A045186 A344034 * A265970 A264291 A265925

Adjacent sequences: A344032 A344033 A344034 * A344036 A344037 A344038

Keyword

nonn

Author

David Consiglio, Jr., May 07 2021

Status

approved