A345185 -id:A345185 - cp's OEIS frontend

A345146 Numbers that are the sum of four third powers in nine or more ways.

21896, 36225, 42120, 46683, 46872, 48321, 48825, 50806, 50904, 51408, 51480, 51506, 51688, 52208, 52416, 53200, 53865, 54971, 55575, 56385, 57113, 58338, 58968, 59059, 60480, 60515, 60984, 62244, 62433, 65303, 66024, 66276, 66339, 66430, 67158, 67536, 67851

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

			42120 is a term because 42120 = 1^3 + 19^3 + 22^3 + 27^3  = 2^3 + 3^3 + 13^3 + 33^3  = 2^3 + 6^3 + 17^3 + 32^3  = 3^3 + 3^3 + 20^3 + 31^3  = 3^3 + 17^3 + 20^3 + 29^3  = 3^3 + 13^3 + 14^3 + 32^3  = 6^3 + 15^3 + 16^3 + 31^3  = 7^3 + 17^3 + 23^3 + 27^3  = 11^3 + 13^3 + 21^3 + 29^3.

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

Cf. A025374, A344926, A345119, A345152, A345154, A345155, A345185.

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 >= 9])
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])

A345518 Numbers that are the sum of six cubes in nine or more ways.

Original entry on oeis.org

2438, 2457, 2494, 2555, 2593, 2709, 2772, 2889, 2942, 2980, 3033, 3043, 3096, 3104, 3160, 3195, 3215, 3222, 3241, 3250, 3257, 3267, 3276, 3313, 3339, 3374, 3402, 3427, 3430, 3437, 3465, 3467, 3491, 3493, 3528, 3547, 3556, 3582, 3584, 3592, 3608, 3609, 3617

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			2457 is a term because 2457 = 1^3 + 1^3 + 2^3 + 4^3 + 4^3 + 12^3 = 1^3 + 2^3 + 2^3 + 3^3 + 5^3 + 12^3 = 1^3 + 3^3 + 3^3 + 4^3 + 7^3 + 11^3 = 1^3 + 5^3 + 5^3 + 7^3 + 7^3 + 9^3 = 2^3 + 2^3 + 3^3 + 6^3 + 6^3 + 11^3 = 2^3 + 3^3 + 3^3 + 3^3 + 9^3 + 10^3 = 2^3 + 5^3 + 5^3 + 6^3 + 6^3 + 10^3 = 3^3 + 3^3 + 5^3 + 8^3 + 8^3 + 8^3 = 3^3 + 3^3 + 4^3 + 7^3 + 8^3 + 9^3.

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

Cf. A345185, A345476, A345517, A345519, A345527, A345566, A345771.

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

A341891 Numbers that are the sum of five fourth powers in nine or more ways.

Original entry on oeis.org

619090, 775714, 954979, 1100579, 1179379, 1186834, 1205539, 1243699, 1357315, 1367539, 1373859, 1422595, 1431234, 1436419, 1511299, 1536019, 1574850, 1699234, 1713859, 1734899, 1801459, 1839874, 1858594, 1863859, 1877394, 1880850, 1882579, 1950355, 1951650

Offset: 1

David Consiglio, Jr., Jun 04 2021

nonn

			619090 =  1^4 +  2^4 + 18^4 + 22^4 + 23^4
       =  1^4 +  3^4 +  4^4 +  8^4 + 28^4
       =  1^4 + 11^4 + 14^4 + 22^4 + 24^4
       =  2^4 +  2^4 +  8^4 + 17^4 + 27^4
       =  2^4 + 13^4 + 13^4 + 18^4 + 26^4
       =  3^4 +  6^4 + 12^4 + 16^4 + 27^4
       =  4^4 + 12^4 + 14^4 + 23^4 + 23^4
       =  9^4 + 12^4 + 16^4 + 21^4 + 24^4
       = 14^4 + 16^4 + 18^4 + 19^4 + 23^4
so 619090 is a term.

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

Cf. A341892, A341897, A344926, A344944, A345185, A345566.

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

A345186 Numbers that are the sum of five third powers in exactly nine ways.

Original entry on oeis.org

6112, 6138, 6462, 6497, 7001, 7038, 7057, 7064, 7099, 7190, 7316, 7328, 7372, 7433, 7561, 7587, 7703, 7759, 7841, 7902, 8163, 8352, 8443, 8560, 8630, 8632, 8928, 8991, 9017, 9136, 9143, 9171, 9288, 9316, 9379, 9505, 9566, 9647, 9658, 9675, 9684, 9745, 9773

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

Differs from A345185 at term 1 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.

			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. A294743, A341892, A345154, A345184, A345185, A345188, A345771.

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])

A345187 Numbers that are the sum of five third powers in ten or more ways.

Original entry on oeis.org

5860, 6588, 6651, 6859, 6947, 8056, 8289, 8371, 8506, 8569, 8758, 9045, 9080, 9099, 9108, 9227, 9414, 9612, 9801, 9829, 9864, 10009, 10018, 10044, 10277, 10466, 10485, 10522, 10529, 10800, 10963, 10970, 10979, 11008, 11017, 11061, 11089, 11152, 11241, 11385

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

			6588 is a term because 6588 = 1^3 + 3^3 + 5^3 + 7^3 + 17^3  = 1^3 + 4^3 + 6^3 + 13^3 + 14^3  = 1^3 + 5^3 + 8^3 + 8^3 + 16^3  = 1^3 + 10^3 + 10^3 + 11^3 + 12^3  = 2^3 + 2^3 + 9^3 + 12^3 + 14^3  = 2^3 + 3^3 + 8^3 + 11^3 + 15^3  = 3^3 + 8^3 + 8^3 + 11^3 + 14^3  = 3^3 + 3^3 + 5^3 + 10^3 + 16^3  = 5^3 + 5^3 + 8^3 + 10^3 + 15^3  = 8^3 + 9^3 + 10^3 + 10^3 + 12^3.

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

Cf. A341897, A344803, A345155, A345185, A345188, A345519.

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 >= 10])
for x in range(len(rets)):
    print(rets[x])

A344802 Numbers that are the sum of five squares in nine or more ways.

Original entry on oeis.org

101, 107, 109, 112, 115, 116, 118, 125, 127, 128, 131, 133, 134, 136, 139, 140, 142, 144, 146, 147, 148, 149, 151, 152, 154, 155, 157, 158, 159, 160, 161, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 178, 179, 180, 181, 182, 183, 184

Offset: 1

Sean A. Irvine, May 29 2021

nonn

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

Cf. A025374, A294743, A344801, A344803, A345185, A345476.

cp's OEIS Frontend

A345146 Numbers that are the sum of four third powers in nine 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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A345518 Numbers that are the sum of six cubes in nine or more ways.

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A341891 Numbers that are the sum of five fourth powers in nine or more ways.

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A345186 Numbers that are the sum of five third powers in exactly nine ways.

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A345187 Numbers that are the sum of five third powers in ten or more ways.

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A344802 Numbers that are the sum of five squares in nine or more ways.

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