A345188 -id:A345188 - cp's OEIS frontend

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

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])

A341898 Numbers that are the sum of five fourth powers in exactly ten ways.

Original entry on oeis.org

954979, 1205539, 1574850, 1713859, 1863859, 1877394, 1882579, 2071939, 2109730, 2225859, 2288179, 2419954, 2492434, 2495939, 2605314, 2711394, 2784499, 2835939, 2847394, 2880994, 2924674, 3007474, 3061939, 3071379, 3074179, 3117235, 3127219, 3174834, 3190899

Offset: 1

David Consiglio, Jr., Jun 04 2021

nonn

Differs at term 5 because
1801459 =  1^4 +  4^4 +  5^4 + 28^4 + 33^4
        =  1^4 +  4^4 + 12^4 + 23^4 + 35^4
        =  1^4 +  7^4 + 16^4 + 30^4 + 31^4
        =  1^4 + 16^4 + 18^4 + 19^4 + 35^4
        =  3^4 +  6^4 + 18^4 + 21^4 + 35^4
        =  5^4 +  7^4 + 19^4 + 24^4 + 34^4
        =  5^4 +  9^4 + 14^4 + 29^4 + 32^4
        =  7^4 +  9^4 + 16^4 + 25^4 + 34^4
        =  7^4 + 14^4 + 16^4 + 21^4 + 35^4
        =  8^4 +  9^4 + 20^4 + 29^4 + 31^4
        = 10^4 + 19^4 + 19^4 + 21^4 + 34^4.

			954979 =  1^4 +  2^4 + 11^4 + 19^4 + 30^4
       =  1^4 +  7^4 + 18^4 + 25^4 + 26^4
       =  3^4 +  8^4 + 17^4 + 20^4 + 29^4
       =  4^4 +  8^4 + 13^4 + 25^4 + 27^4
       =  4^4 +  9^4 + 10^4 + 11^4 + 31^4
       =  6^4 +  6^4 + 15^4 + 21^4 + 29^4
       =  7^4 + 10^4 + 18^4 + 19^4 + 29^4
       = 11^4 + 11^4 + 20^4 + 22^4 + 27^4
       = 16^4 + 17^4 + 17^4 + 24^4 + 25^4
       = 18^4 + 19^4 + 20^4 + 23^4 + 23^4
so 954979 is a term.

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

Cf. A341892, A341897, A344929, A345188, A345822.

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

A345156 Numbers that are the sum of four third powers in exactly ten ways.

Original entry on oeis.org

21896, 36225, 48825, 51506, 52416, 53200, 58338, 58968, 60480, 66024, 67851, 70434, 70525, 71155, 72819, 76923, 78624, 78912, 85995, 87507, 88641, 90181, 90783, 91728, 93555, 97552, 98280, 98560, 99008, 99225, 99792, 100170, 103040, 104104, 104265, 104958

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

Differs from A345155 at term 3 because 46872 = 1^3 + 16^3 + 22^3 + 30^3 = 2^3 + 11^3 + 17^3 + 33^3 = 3^3 + 3^3 + 4^3 + 35^3 = 3^3 + 4^3 + 26^3 + 29^3 = 3^3 + 5^3 + 23^3 + 31^3 = 4^3 + 10^3 + 24^3 + 30^3 = 5^3 + 17^3 + 23^3 + 29^3 = 6^3 + 10^3 + 20^3 + 32^3 = 11^3 + 11^3 + 21^3 + 31^3 = 11^3 + 14^3 + 17^3 + 32^3 = 19^3 + 21^3 + 21^3 + 25^3.

			21896 is a term because 21896 = 1^3 + 11^3 + 19^3 + 22^3  = 2^3 + 2^3 + 12^3 + 26^3  = 2^3 + 3^3 + 19^3 + 23^3  = 2^3 + 5^3 + 15^3 + 25^3  = 3^3 + 10^3 + 16^3 + 24^3  = 3^3 + 17^3 + 19^3 + 19^3  = 4^3 + 6^3 + 20^3 + 22^3  = 5^3 + 8^3 + 14^3 + 25^3  = 7^3 + 11^3 + 17^3 + 23^3  = 8^3 + 9^3 + 19^3 + 22^3.

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

Cf. A025366, A344929, A345122, A345154, A345155, A345188.

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

A345772 Numbers that are the sum of six cubes in exactly ten ways.

Original entry on oeis.org

3215, 3267, 3313, 3339, 3374, 3465, 3493, 3528, 3547, 3584, 3645, 3654, 3698, 3736, 3745, 3752, 3754, 3780, 3789, 3843, 3869, 3878, 3880, 3888, 3906, 3915, 3923, 3950, 3995, 4004, 4014, 4041, 4067, 4122, 4148, 4211, 4212, 4214, 4265, 4266, 4268, 4338, 4349

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345519 at term 1 because 3104 = 1^3 + 2^3 + 7^3 + 8^3 + 8^3 + 12^3 = 1^3 + 5^3 + 5^3 + 5^3 + 10^3 + 12^3 = 2^3 + 2^3 + 4^3 + 4^3 + 6^3 + 14^3 = 2^3 + 3^3 + 4^3 + 7^3 + 11^3 + 11^3 = 2^3 + 3^3 + 5^3 + 6^3 + 10^3 + 12^3 = 2^3 + 7^3 + 8^3 + 8^3 + 9^3 + 10^3 = 3^3 + 3^3 + 5^3 + 6^3 + 8^3 + 13^3 = 4^3 + 5^3 + 7^3 + 8^3 + 9^3 + 11^3 = 5^3 + 5^3 + 5^3 + 9^3 + 10^3 + 10^3 = 5^3 + 6^3 + 6^3 + 6^3 + 10^3 + 11^3 = 6^3 + 6^3 + 6^3 + 6^3 + 8^3 + 12^3.

			3215 is a term because 3215 = 1^3 + 1^3 + 1^3 + 4^3 + 6^3 + 13^3 = 1^3 + 1^3 + 2^3 + 2^3 + 9^3 + 12^3 = 1^3 + 1^3 + 3^3 + 8^3 + 8^3 + 11^3 = 1^3 + 2^3 + 3^3 + 5^3 + 8^3 + 12^3 = 1^3 + 3^3 + 3^3 + 3^3 + 10^3 + 11^3 = 1^3 + 3^3 + 8^3 + 8^3 + 8^3 + 9^3 = 2^3 + 3^3 + 6^3 + 6^3 + 8^3 + 11^3 = 3^3 + 3^3 + 3^3 + 8^3 + 9^3 + 10^3 = 3^3 + 5^3 + 5^3 + 5^3 + 6^3 + 12^3 = 6^3 + 6^3 + 6^3 + 6^3 + 7^3 + 10^3.

Sean A. Irvine, Table of n, a(n) for n = 1..1454

Cf. A345188, A345519, A345771, A345782, A345822.

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

cp's OEIS Frontend

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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A341898 Numbers that are the sum of five fourth powers in exactly ten ways.

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A345156 Numbers that are the sum of four third powers in exactly ten ways.

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A345772 Numbers that are the sum of six cubes in exactly ten ways.

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