A345180 -id:A345180 - cp's OEIS frontend

A345150 Numbers that are the sum of four third powers in seven or more ways.

13104, 18928, 19376, 20755, 21203, 21896, 22743, 24544, 24570, 24787, 25172, 25928, 27720, 27755, 27846, 28917, 29582, 30429, 31031, 31248, 31339, 31402, 31528, 32858, 33579, 34056, 34624, 34713, 34776, 35289, 35317, 35441, 35497, 35712, 36162, 36190, 36225

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

			13104 is a term because 13104 = 1^3 + 10^3 + 16^3 + 18^3  = 1^3 + 11^3 + 14^3 + 19^3  = 2^3 + 9^3 + 15^3 + 19^3  = 4^3 + 6^3 + 14^3 + 20^3  = 4^3 + 9^3 + 10^3 + 21^3  = 5^3 + 7^3 + 11^3 + 21^3  = 8^3 + 9^3 + 14^3 + 19^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A025372, A344922, A345086, A345148, A345151, A345152, A345180.

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, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 7])
for x in range(len(rets)):
    print(rets[x])

A345174 Numbers that are the sum of five third powers in six or more ways.

Original entry on oeis.org

2430, 2979, 3214, 3249, 3312, 3492, 3520, 3737, 3753, 3788, 3816, 3842, 3942, 3968, 4121, 4185, 4213, 4267, 4355, 4392, 4411, 4418, 4446, 4453, 4456, 4465, 4472, 4482, 4509, 4544, 4563, 4600, 4626, 4663, 4670, 4723, 4753, 4896, 4905, 4915, 4924, 4938, 4941

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

			2430 is a term because 2430 = 1^3 + 2^3 + 2^3 + 5^3 + 12^3  = 1^3 + 3^3 + 4^3 + 7^3 + 11^3  = 2^3 + 2^3 + 6^3 + 6^3 + 11^3  = 2^3 + 3^3 + 3^3 + 9^3 + 10^3  = 3^3 + 5^3 + 8^3 + 8^3 + 8^3  = 3^3 + 4^3 + 7^3 + 8^3 + 9^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A343989, A344799, A344940, A345148, A345175, A345180, A345515.

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, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 6])
for x in range(len(rets)):
    print(rets[x])

A345183 Numbers that are the sum of five third powers in eight or more ways.

Original entry on oeis.org

4392, 4915, 5139, 5256, 5321, 5624, 5643, 5678, 5741, 5769, 5797, 5832, 5860, 5914, 6075, 6112, 6138, 6202, 6462, 6497, 6499, 6560, 6588, 6616, 6642, 6651, 6677, 6833, 6859, 6884, 6947, 7001, 7008, 7038, 7057, 7064, 7099, 7111, 7128, 7155, 7190, 7218, 7316

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

			4915 is a term because 4915 = 1^3 + 2^3 + 7^3 + 12^3 + 12^3  = 1^3 + 3^3 + 7^3 + 9^3 + 14^3  = 1^3 + 8^3 + 8^3 + 11^3 + 11^3  = 2^3 + 4^3 + 6^3 + 6^3 + 15^3  = 3^3 + 3^3 + 5^3 + 7^3 + 15^3  = 3^3 + 3^3 + 10^3 + 11^3 + 11^3  = 4^3 + 6^3 + 6^3 + 8^3 + 14^3  = 8^3 + 8^3 + 8^3 + 9^3 + 11^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A344801, A344944, A345152, A345180, A345184, A345185, A345517.

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

A345516 Numbers that are the sum of six cubes in seven or more ways.

Original entry on oeis.org

1710, 1766, 1773, 1981, 1988, 2051, 2105, 2160, 2168, 2196, 2249, 2251, 2259, 2277, 2314, 2322, 2349, 2368, 2375, 2376, 2417, 2424, 2431, 2438, 2457, 2466, 2480, 2492, 2494, 2513, 2520, 2531, 2538, 2539, 2548, 2555, 2557, 2564, 2565, 2574, 2583, 2593, 2611

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			1766 is a term because 1766 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 11^3 = 1^3 + 1^3 + 1^3 + 5^3 + 5^3 + 10^3 = 1^3 + 1^3 + 2^3 + 3^3 + 8^3 + 9^3 = 1^3 + 3^3 + 3^3 + 5^3 + 8^3 + 8^3 = 1^3 + 3^3 + 3^3 + 4^3 + 7^3 + 9^3 = 2^3 + 2^3 + 3^3 + 6^3 + 6^3 + 9^3 = 3^3 + 3^3 + 3^3 + 3^3 + 5^3 + 10^3.

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

Cf. A344811, A345180, A345515, A345517, A345525, A345564, A345769.

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 >= 7])
    for x in range(len(rets)):
        print(rets[x])

A344942 Numbers that are the sum of five fourth powers in seven or more ways.

Original entry on oeis.org

197779, 211059, 217154, 236675, 431155, 444019, 480739, 503539, 530659, 534130, 548994, 564979, 568450, 571539, 602450, 602770, 619090, 621859, 625635, 625939, 626194, 650659, 651954, 653059, 654130, 654754, 663155, 666739, 687314, 692754, 692899, 698019

Offset: 1

David Consiglio, Jr., Jun 03 2021

nonn

			197779 is a term because 197779 = 1^4 + 5^4 + 6^4 + 16^4 + 19^4  = 1^4 + 7^4 + 11^4 + 12^4 + 20^4  = 1^4 + 10^4 + 12^4 + 17^4 + 17^4  = 2^4 + 4^4 + 5^4 + 7^4 + 21^4  = 3^4 + 5^4 + 6^4 + 6^4 + 21^4  = 4^4 + 7^4 + 9^4 + 13^4 + 20^4  = 11^4 + 13^4 + 14^4 + 15^4 + 16^4.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A344922, A344940, A344943, A344944, A345180, A345564.

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, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 7])
for x in range(len(rets)):
    print(rets[x])

A345181 Numbers that are the sum of five third powers in exactly seven ways.

Original entry on oeis.org

4472, 4544, 4600, 4957, 5076, 5113, 5120, 5132, 5165, 5174, 5347, 5354, 5384, 5391, 5410, 5445, 5474, 5481, 5507, 5543, 5617, 5715, 5760, 5834, 5895, 5923, 5984, 5986, 6049, 6128, 6131, 6245, 6280, 6373, 6407, 6434, 6436, 6544, 6553, 6733, 6768, 6831, 6840

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

Differs from A345180 at term 1 because 4392 = 1^3 + 1^3 + 10^3 + 10^3 + 11^3 = 1^3 + 2^3 + 2^3 + 9^3 + 14^3 = 1^3 + 8^3 + 9^3 + 10^3 + 10^3 = 2^3 + 2^3 + 3^3 + 5^3 + 15^3 = 2^3 + 3^3 + 5^3 + 8^3 + 14^3 = 2^3 + 8^3 + 8^3 + 8^3 + 12^3 = 3^3 + 6^3 + 7^3 + 8^3 + 13^3 = 5^3 + 5^3 + 5^3 + 9^3 + 13^3.

			4472 is a term because 4472 = 1^3 + 4^3 + 4^3 + 4^3 + 15^3  = 2^3 + 2^3 + 9^3 + 11^3 + 11^3  = 2^3 + 3^3 + 4^3 + 5^3 + 15^3  = 2^3 + 3^3 + 7^3 + 11^3 + 12^3  = 3^3 + 3^3 + 6^3 + 10^3 + 13^3  = 3^3 + 4^3 + 5^3 + 8^3 + 14^3  = 5^3 + 5^3 + 7^3 + 10^3 + 12^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A294741, A344943, A345151, A345175, A345180, A345184, A345769.

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, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 7])
for x in range(len(rets)):
    print(rets[x])

A344800 Numbers that are the sum of five squares in seven or more ways.

Original entry on oeis.org

77, 83, 85, 88, 91, 94, 99, 101, 104, 106, 107, 109, 112, 115, 116, 118, 119, 120, 122, 123, 124, 125, 126, 127, 128, 130, 131, 133, 134, 136, 137, 138, 139, 140, 141, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 161

Offset: 1

Sean A. Irvine, May 28 2021

nonn

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

Cf. A025372, A294741, A344799, A344801, A344811, A345180.

cp's OEIS Frontend

A345150 Numbers that are the sum of four third powers in seven or more ways.

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A345174 Numbers that are the sum of five third powers in six or more ways.

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A345183 Numbers that are the sum of five third powers in eight or more ways.

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A345516 Numbers that are the sum of six cubes in seven or more ways.

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A344942 Numbers that are the sum of five fourth powers in seven or more ways.

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A345181 Numbers that are the sum of five third powers in exactly seven ways.

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A344800 Numbers that are the sum of five squares in seven or more ways.

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