A345183 -id:A345183 - cp's OEIS frontend

A345152 Numbers that are the sum of four third powers in eight or more ways.

21896, 27720, 30429, 31339, 31402, 33579, 34624, 34776, 36162, 36225, 40105, 42120, 42695, 44037, 44163, 44226, 44947, 45162, 45675, 46277, 46683, 46872, 46900, 47600, 48321, 48825, 49042, 50112, 50689, 50806, 50904, 51058, 51408, 51480, 51506, 51597, 51688

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

			30429 is a term because 30429 = 1^3 + 4^3 + 7^3 + 30^3  = 1^3 + 16^3 + 17^3 + 26^3  = 2^3 + 12^3 + 21^3 + 25^3  = 3^3 + 3^3 + 14^3 + 29^3  = 4^3 + 17^3 + 21^3 + 23^3  = 5^3 + 11^3 + 15^3 + 28^3  = 6^3 + 6^3 + 22^3 + 25^3  = 7^3 + 14^3 + 18^3 + 26^3.

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

Cf. A025373, A344924, A345087, A345146, A345150, A345153, A345183.

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 >= 8])
for x in range(len(rets)):
    print(rets[x])

A345180 Numbers that are the sum of five third powers in seven or more ways.

Original entry on oeis.org

4392, 4472, 4544, 4600, 4915, 4957, 5076, 5113, 5120, 5132, 5139, 5165, 5174, 5256, 5321, 5347, 5354, 5384, 5391, 5410, 5445, 5474, 5481, 5507, 5543, 5617, 5624, 5643, 5678, 5715, 5741, 5760, 5769, 5797, 5832, 5834, 5860, 5895, 5914, 5923, 5984, 5986, 6049

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

			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. A344800, A344942, A345150, A345174, A345181, A345183, A345516.

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])

A345185 Numbers that are the sum of five third powers in nine or more ways.

Original entry on oeis.org

5860, 6112, 6138, 6462, 6497, 6588, 6651, 6859, 6947, 7001, 7038, 7057, 7064, 7099, 7190, 7316, 7328, 7372, 7433, 7561, 7587, 7703, 7759, 7841, 7902, 8056, 8163, 8289, 8352, 8371, 8443, 8506, 8560, 8569, 8630, 8632, 8758, 8928, 8991, 9017, 9045, 9080, 9099

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

			6112 is a term because 6112 = 1^3 + 2^3 + 9^3 + 11^3 + 14^3  = 1^3 + 3^3 + 7^3 + 12^3 + 14^3  = 1^3 + 6^3 + 6^3 + 7^3 + 16^3  = 2^3 + 2^3 + 9^3 + 9^3 + 15^3  = 2^3 + 3^3 + 5^3 + 11^3 + 15^3  = 2^3 + 8^3 + 9^3 + 9^3 + 14^3  = 3^3 + 3^3 + 3^3 + 4^3 + 17^3  = 3^3 + 5^3 + 8^3 + 11^3 + 14^3  = 8^3 + 8^3 + 8^3 + 11^3 + 12^3.

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

Cf. A341891, A344802, A345146, A345183, A345186, A345187, A345518.

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 >= 9])
for x in range(len(rets)):
    print(rets[x])

A345517 Numbers that are the sum of six cubes in eight or more ways.

Original entry on oeis.org

1981, 2105, 2168, 2277, 2368, 2376, 2431, 2438, 2457, 2466, 2494, 2538, 2555, 2557, 2583, 2593, 2646, 2665, 2672, 2709, 2746, 2753, 2763, 2765, 2772, 2880, 2881, 2889, 2916, 2942, 2961, 2970, 2977, 2979, 2980, 2987, 3007, 3033, 3040, 3042, 3043, 3049, 3068

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			2105 is a term because 2105 = 1^3 + 1^3 + 4^3 + 4^3 + 4^3 + 11^3 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 11^3 = 1^3 + 2^3 + 6^3 + 7^3 + 7^3 + 8^3 = 1^3 + 4^3 + 4^3 + 4^3 + 8^3 + 9^3 = 1^3 + 4^3 + 5^3 + 5^3 + 5^3 + 10^3 = 2^3 + 3^3 + 4^3 + 5^3 + 8^3 + 9^3 = 3^3 + 3^3 + 3^3 + 7^3 + 7^3 + 9^3 = 5^3 + 5^3 + 5^3 + 5^3 + 7^3 + 8^3.

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

Cf. A344812, A345183, A345516, A345518, A345526, A345565, A345770.

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 >= 8])
    for x in range(len(rets)):
        print(rets[x])

A344944 Numbers that are the sum of five fourth powers in eight or more ways.

Original entry on oeis.org

534130, 619090, 654754, 663155, 729219, 737459, 742770, 758354, 775714, 810034, 813459, 816579, 831250, 906034, 930499, 954930, 954979, 1009954, 1055619, 1083955, 1099459, 1100579, 1101859, 1103554, 1106019, 1157634, 1167794, 1179379, 1180003, 1186834

Offset: 1

David Consiglio, Jr., Jun 03 2021

nonn

			534130 is a term because 534130 = 1^4 + 3^4 + 16^4 + 22^4 + 22^4  = 2^4 + 2^4 + 4^4 + 7^4 + 27^4  = 2^4 + 3^4 + 6^4 + 6^4 + 27^4  = 2^4 + 6^4 + 9^4 + 21^4 + 24^4  = 4^4 + 16^4 + 17^4 + 18^4 + 23^4  = 6^4 + 8^4 + 11^4 + 22^4 + 23^4  = 7^4 + 8^4 + 16^4 + 19^4 + 24^4  = 13^4 + 14^4 + 14^4 + 21^4 + 22^4.

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

Cf. A341891, A344922, A344924, A344942, A344945, A345183, A345565.

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 >= 8])
for x in range(len(rets)):
    print(rets[x])

A345184 Numbers that are the sum of five third powers in exactly eight ways.

Original entry on oeis.org

4392, 4915, 5139, 5256, 5321, 5624, 5643, 5678, 5741, 5769, 5797, 5832, 5914, 6075, 6202, 6499, 6560, 6616, 6642, 6677, 6833, 6884, 7008, 7111, 7128, 7155, 7218, 7344, 7395, 7641, 7696, 7729, 7785, 7813, 7820, 7849, 7883, 8037, 8100, 8243, 8282, 8308, 8315

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

Differs from A345183 at term 13 because 5860 = 1^3 + 1^3 + 5^3 + 8^3 + 16^3 = 1^3 + 2^3 + 3^3 + 11^3 + 15^3 = 1^3 + 3^3 + 8^3 + 11^3 + 14^3 = 1^3 + 5^3 + 5^3 + 10^3 + 15^3 = 1^3 + 9^3 + 10^3 + 10^3 + 12^3 = 2^3 + 3^3 + 8^3 + 9^3 + 15^3 = 2^3 + 3^3 + 5^3 + 12^3 + 14^3 = 2^3 + 8^3 + 8^3 + 12^3 + 12^3 = 3^3 + 8^3 + 8^3 + 9^3 + 14^3 = 3^3 + 6^3 + 7^3 + 12^3 + 13^3.

			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. A294742, A344945, A345153, A345181, A345183, A345186, A345770.

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])

A344801 Numbers that are the sum of five squares in eight or more ways.

Original entry on oeis.org

91, 101, 104, 106, 107, 109, 112, 115, 116, 118, 119, 122, 123, 125, 126, 127, 128, 131, 133, 134, 136, 139, 140, 141, 142, 143, 144, 146, 147, 148, 149, 151, 152, 154, 155, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173

Offset: 1

Sean A. Irvine, May 29 2021

nonn

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

Cf. A025373, A294742, A344800, A344802, A344812, A345183.

cp's OEIS Frontend

A345152 Numbers that are the sum of four third powers in eight or more ways.

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A345180 Numbers that are the sum of five third powers in seven or more ways.

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A345185 Numbers that are the sum of five third powers in nine or more ways.

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A345517 Numbers that are the sum of six cubes in eight or more ways.

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A344944 Numbers that are the sum of five fourth powers in eight or more ways.

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A345184 Numbers that are the sum of five third powers in exactly eight ways.

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A344801 Numbers that are the sum of five squares in eight or more ways.

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