A345513 -id:A345513 - cp's OEIS frontend

A344034 Numbers that are the sum of five positive cubes in four or more ways.

1252, 1376, 1461, 1522, 1548, 1585, 1590, 1646, 1702, 1709, 1737, 1739, 1765, 1772, 1798, 1802, 1810, 1864, 1889, 1954, 1980, 1987, 2006, 2033, 2043, 2081, 2096, 2104, 2152, 2160, 2195, 2225, 2241, 2250, 2251, 2276, 2313, 2322, 2339, 2341, 2367, 2374, 2377, 2416, 2423, 2430, 2449, 2456, 2458, 2465, 2467, 2486

Offset: 1

David Consiglio, Jr., May 07 2021

nonn

			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
so 1461 is a term of this sequence.

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

Cf. A343704, A343971, A343989, A344035, A344354, A344797, A345513.

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])

A345512 Numbers that are the sum of six cubes in three or more ways.

Original entry on oeis.org

221, 254, 369, 411, 443, 469, 495, 502, 576, 595, 600, 626, 648, 658, 684, 704, 711, 720, 739, 746, 753, 760, 765, 767, 772, 774, 779, 786, 793, 811, 818, 828, 830, 835, 837, 844, 854, 856, 863, 866, 873, 874, 880, 884, 886, 891, 892, 893, 899, 905, 910, 919

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			254 is a term because 254 = 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 4^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 5^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.

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

Cf. A048931, A343704, A344807, A345511, A345513, A345521, A345560.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 3])
    for x in range(len(rets)):
        print(rets[x])

A345514 Numbers that are the sum of six cubes in five or more ways.

Original entry on oeis.org

1045, 1169, 1241, 1260, 1377, 1384, 1432, 1440, 1488, 1495, 1530, 1539, 1549, 1556, 1558, 1584, 1586, 1594, 1595, 1602, 1612, 1617, 1640, 1647, 1654, 1657, 1673, 1675, 1677, 1703, 1710, 1712, 1715, 1719, 1729, 1736, 1738, 1745, 1747, 1754, 1764, 1766, 1771

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			1169 is a term because 1169 = 1^3 + 2^3 + 2^3 + 3^3 + 4^3 + 9^3 = 1^3 + 2^3 + 5^3 + 5^3 + 5^3 + 7^3 = 1^3 + 3^3 + 4^3 + 4^3 + 4^3 + 8^3 = 2^3 + 3^3 + 3^3 + 4^3 + 5^3 + 8^3 = 3^3 + 3^3 + 3^3 + 3^3 + 7^3 + 7^3.

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

Cf. A343989, A344809, A345513, A345515, A345523, A345562, A345767.

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, 6):
    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])

A345522 Numbers that are the sum of seven cubes in four or more ways.

Original entry on oeis.org

470, 496, 503, 603, 627, 634, 653, 659, 685, 690, 692, 711, 712, 747, 751, 754, 761, 766, 768, 773, 775, 777, 780, 783, 787, 792, 794, 812, 813, 829, 831, 836, 838, 842, 843, 845, 857, 859, 864, 867, 871, 874, 875, 881, 883, 885, 890, 892, 894, 899, 900, 901

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			496 is a term because 496 = 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 5^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 5^3 + 5^3 = 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 6^3 = 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3.

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

Cf. A345481, A345513, A345521, A345523, A345534, A345570, A345776.

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, 7):
    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])

A345561 Numbers that are the sum of six fourth powers in four or more ways.

Original entry on oeis.org

6626, 6691, 6866, 9251, 9491, 10115, 10706, 10786, 11555, 12595, 14225, 14691, 14771, 15315, 15330, 15395, 15570, 16051, 16595, 16610, 16660, 16675, 16850, 17090, 17091, 17236, 17316, 17331, 17346, 17860, 17875, 17940, 17955, 18195, 18786, 18851, 18866, 19155

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			6691 is a term because 6691 = 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 = 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 = 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4.

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

Cf. A344354, A345513, A345560, A345562, A345570, A345718, A345816.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
    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])

A345766 Numbers that are the sum of six cubes in exactly four ways.

Original entry on oeis.org

626, 830, 837, 856, 873, 891, 947, 954, 982, 1008, 1026, 1052, 1053, 1071, 1094, 1097, 1106, 1109, 1134, 1143, 1150, 1153, 1172, 1195, 1208, 1227, 1234, 1253, 1267, 1278, 1279, 1283, 1286, 1290, 1297, 1316, 1323, 1324, 1358, 1361, 1368, 1369, 1376, 1395, 1403

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345513 at term 12 because 1045 = 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 10^3 = 1^3 + 1^3 + 4^3 + 5^3 + 5^3 + 9^3 = 1^3 + 2^3 + 3^3 + 4^3 + 6^3 + 9^3 = 3^3 + 3^3 + 6^3 + 6^3 + 6^3 + 7^3 = 4^3 + 4^3 + 4^3 + 5^3 + 6^3 + 8^3.

			830 is a term because 830 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 8^3 = 1^3 + 3^3 + 3^3 + 5^3 + 5^3 + 6^3 = 1^3 + 3^3 + 3^3 + 3^3 + 4^3 + 7^3 = 2^3 + 2^3 + 3^3 + 3^3 + 6^3 + 6^3.

Sean A. Irvine, Table of n, a(n) for n = 1..1211

Cf. A048931, A344035, A345513, A345767, A345776, A345816.

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, 6):
    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])

A344808 Numbers that are the sum of six squares in four or more ways.

Original entry on oeis.org

36, 41, 44, 45, 53, 54, 56, 57, 60, 62, 63, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			41 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 6^2
   = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 5^2
   = 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 3^2
   = 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 4^2
so 41 is a term.

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Cf. A344797, A344807, A344809, A345481, A345513.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
    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])

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A344034 Numbers that are the sum of five positive cubes in four or more ways.

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A345512 Numbers that are the sum of six cubes in three or more ways.

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A345514 Numbers that are the sum of six cubes in five or more ways.

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A345522 Numbers that are the sum of seven cubes in four or more ways.

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A345561 Numbers that are the sum of six fourth powers in four or more ways.

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A345766 Numbers that are the sum of six cubes in exactly four ways.

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A344808 Numbers that are the sum of six squares in four or more ways.

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