A345593 -id:A345593 - cp's OEIS frontend

A345584 Numbers that are the sum of eight fourth powers in nine or more ways.

15427, 16692, 17348, 17493, 17972, 17987, 18052, 18227, 19267, 19412, 19492, 19507, 19572, 19747, 19748, 20116, 20787, 20852, 21268, 21283, 21333, 21348, 21413, 21443, 21493, 21508, 21523, 21588, 21637, 21652, 21653, 21827, 21877, 21892, 21957, 21972, 22037

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			16692 is a term because 16692 = 1^4 + 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 10^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 + 10^4 = 1^4 + 1^4 + 2^4 + 5^4 + 6^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 11^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 10^4 = 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4 = 1^4 + 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 2^4 + 4^4 + 4^4 + 5^4 + 7^4 + 9^4 + 9^4 = 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 9^4 + 9^4.

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

Cf. A345539, A345575, A345583, A345585, A345593, A345617, A345841.

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, 8):
    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])

A345592 Numbers that are the sum of nine fourth powers in eight or more ways.

Original entry on oeis.org

6804, 6869, 8019, 8084, 8259, 8324, 8499, 8564, 9044, 9124, 9219, 9234, 9284, 9299, 9364, 9429, 9474, 9494, 9539, 9604, 9669, 9749, 9779, 10148, 10259, 10293, 10339, 10388, 10453, 10514, 10579, 10628, 10644, 10709, 10754, 10789, 10819, 10884, 10949, 10964

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			6869 is a term because 6869 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 9^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 9^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4.

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

Cf. A345547, A345583, A345591, A345593, A345601, A345625, A345850.

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, 9):
    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])

A345851 Numbers that are the sum of nine fourth powers in exactly nine ways.

Original entry on oeis.org

8259, 9539, 10709, 10819, 10884, 10949, 10964, 11124, 11444, 11573, 11668, 11684, 11924, 12099, 12164, 12339, 12404, 12549, 12773, 12853, 12918, 13013, 13139, 13204, 13284, 13379, 13444, 13509, 13958, 13988, 14053, 14213, 14293, 14308, 14373, 14403, 14484

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345593 at term 2 because 9299 = 1^4 + 1^4 + 1^4 + 2^4 + 6^4 + 6^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 7^4 + 8^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 7^4 + 8^4 = 2^4 + 2^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 7^4 = 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 + 9^4 = 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4.

			9299 is a term because 9299 = 1^4 + 1^4 + 1^4 + 2^4 + 6^4 + 6^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 7^4 + 8^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 7^4 + 8^4 = 2^4 + 2^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 7^4 = 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 + 9^4 = 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4.

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

Cf. A345593, A345801, A345841, A345850, A345852, A345861, A346344.

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, 9):
    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])

A345548 Numbers that are the sum of nine cubes in nine or more ways.

Original entry on oeis.org

859, 861, 896, 903, 922, 929, 935, 939, 959, 966, 971, 973, 978, 985, 992, 997, 999, 1004, 1009, 1011, 1016, 1018, 1020, 1022, 1023, 1027, 1029, 1030, 1034, 1035, 1036, 1037, 1041, 1046, 1048, 1055, 1056, 1059, 1060, 1062, 1063, 1064, 1065, 1066, 1067, 1071

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			861 is a term because 861 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 8^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 5^3 + 7^3 = 1^3 + 1^3 + 2^3 + 2^3 + 4^3 + 4^3 + 4^3 + 4^3 + 6^3 = 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 7^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 8^3 = 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 + 4^3 + 5^3 + 6^3 = 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 5^3 + 5^3 + 6^3 = 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 4^3 + 7^3 = 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3.

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

Cf. A345539, A345547, A345549, A345557, A345593, A345801.

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, 9):
    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])

A345594 Numbers that are the sum of nine fourth powers in ten or more ways.

Original entry on oeis.org

9299, 12708, 12948, 13269, 13349, 13524, 13589, 13764, 13829, 13893, 14133, 14228, 14468, 14564, 14804, 14869, 14934, 14964, 15014, 15044, 15094, 15109, 15174, 15189, 15333, 15413, 15428, 15429, 15443, 15508, 15524, 15573, 15588, 15604, 15653, 15669, 15683

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			12708 is a term because 12708 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 10^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 10^4 = 1^4 + 1^4 + 1^4 + 5^4 + 6^4 + 6^4 + 6^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 8^4 + 9^4 = 1^4 + 2^4 + 4^4 + 4^4 + 5^4 + 6^4 + 6^4 + 7^4 + 9^4 = 1^4 + 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 6^4 + 6^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4 + 10^4 = 2^4 + 2^4 + 3^4 + 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 = 2^4 + 4^4 + 4^4 + 4^4 + 5^4 + 7^4 + 7^4 + 7^4 + 8^4 = 3^4 + 4^4 + 4^4 + 5^4 + 6^4 + 6^4 + 7^4 + 7^4 + 8^4.

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

Cf. A345549, A345585, A345593, A345603, A345627, A345852.

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, 9):
    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])

A345602 Numbers that are the sum of ten fourth powers in nine or more ways.

Original entry on oeis.org

6820, 6870, 6885, 6950, 7060, 7110, 7125, 7285, 7350, 7860, 7925, 7990, 8020, 8035, 8100, 8165, 8230, 8245, 8260, 8275, 8325, 8340, 8390, 8405, 8515, 8565, 8580, 8645, 8755, 8820, 8884, 8965, 8995, 9030, 9045, 9060, 9075, 9125, 9140, 9205, 9220, 9235, 9270

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			6870 is a term because 6870 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 9^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 = 2^4 + 2^4 + 2^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 6^4 + 7^4.

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

Cf. A345557, A345593, A345601, A345603, A345641, A345861.

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, 10):
    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])

A345626 Numbers that are the sum of nine fifth powers in nine or more ways.

Original entry on oeis.org

1969221, 2596936, 3353186, 3378178, 3923426, 3981447, 4094027, 4096729, 4112329, 4114188, 4129465, 4137209, 4147736, 4157156, 4170112, 4172994, 4254304, 4303773, 4410482, 4475846, 4477936, 4483379, 4485480, 4492410, 4501441, 4510461, 4543232, 4652011, 4691855

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			2596936 is a term because 2596936 = 1^5 + 1^5 + 4^5 + 5^5 + 9^5 + 13^5 + 13^5 + 13^5 + 17^5 = 1^5 + 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 17^5 = 1^5 + 4^5 + 7^5 + 7^5 + 7^5 + 9^5 + 9^5 + 14^5 + 18^5 = 1^5 + 5^5 + 6^5 + 6^5 + 8^5 + 9^5 + 9^5 + 14^5 + 18^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 12^5 + 13^5 + 14^5 + 17^5 = 2^5 + 5^5 + 5^5 + 6^5 + 6^5 + 6^5 + 15^5 + 15^5 + 16^5 = 3^5 + 3^5 + 5^5 + 6^5 + 7^5 + 9^5 + 12^5 + 13^5 + 18^5 = 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 11^5 + 11^5 + 13^5 + 18^5 = 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 8^5 + 9^5 + 16^5 + 17^5.

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

Cf. A345593, A345617, A345625, A345627, A345641, A346344.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 9):
    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])

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A345584 Numbers that are the sum of eight fourth powers in nine or more ways.

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A345592 Numbers that are the sum of nine fourth powers in eight or more ways.

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A345851 Numbers that are the sum of nine fourth powers in exactly nine ways.

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A345548 Numbers that are the sum of nine cubes in nine or more ways.

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A345594 Numbers that are the sum of nine fourth powers in ten or more ways.

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A345602 Numbers that are the sum of ten fourth powers in nine or more ways.

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A345626 Numbers that are the sum of nine fifth powers in nine or more ways.

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