A345571 -id:A345571 - cp's OEIS frontend

A345523 Numbers that are the sum of seven cubes in five or more ways.

627, 768, 838, 845, 857, 864, 874, 881, 894, 900, 920, 937, 950, 955, 962, 969, 976, 981, 983, 990, 1002, 1009, 1011, 1016, 1027, 1046, 1053, 1054, 1060, 1061, 1063, 1072, 1079, 1089, 1096, 1098, 1102, 1105, 1107, 1109, 1115, 1117, 1121, 1124, 1128, 1133

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			768 is a term because 768 = 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 8^3 = 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 4^3 + 7^3 = 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 6^3 + 6^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 5^3 + 7^3 = 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 5^3 + 6^3.

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

Cf. A345482, A345514, A345522, A345524, A345535, A345571, A345777.

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

A345562 Numbers that are the sum of six fourth powers in five or more ways.

Original entry on oeis.org

15395, 16610, 18866, 19235, 19410, 20996, 21011, 21251, 21316, 21331, 21491, 21620, 23811, 25091, 29700, 29715, 29906, 29955, 30356, 30995, 31235, 31266, 31331, 31506, 32035, 33651, 33795, 33891, 35171, 35411, 35636, 35796, 35971, 37811, 37971, 38051, 38595

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			16610 is a term because 16610 = 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 10^4 = 2^4 + 2^4 + 2^4 + 5^4 + 6^4 + 11^4 = 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 10^4 = 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4 = 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4.

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

Cf. A344358, A345514, A345561, A345563, A345571, A345719, A345817.

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

A345570 Numbers that are the sum of seven fourth powers in four or more ways.

Original entry on oeis.org

2932, 4147, 4212, 4387, 5427, 5602, 5667, 6627, 6642, 6692, 6707, 6772, 6817, 6822, 6837, 6852, 6867, 6882, 6947, 7012, 7122, 7251, 7316, 7491, 7747, 7857, 7922, 7987, 8052, 8097, 8162, 8227, 8402, 8467, 8532, 8707, 8787, 8962, 9027, 9092, 9157, 9172, 9202

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			4147 is a term because 4147 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4.

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

Cf. A345522, A345561, A345569, A345571, A345579, A345607, A345826.

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

A345572 Numbers that are the sum of seven fourth powers in six or more ways.

Original entry on oeis.org

10787, 15396, 15411, 15586, 15651, 16611, 16626, 16676, 16691, 16866, 17347, 17956, 17971, 18867, 19156, 19236, 19251, 19411, 19426, 19491, 19666, 20035, 20706, 20771, 21012, 21187, 21252, 21267, 21332, 21397, 21412, 21442, 21492, 21507, 21572, 21621, 21636

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			15396 is a term because 15396 = 1^4 + 1^4 + 1^4 + 1^4 + 6^4 + 8^4 + 10^4 = 1^4 + 1^4 + 2^4 + 5^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 11^4 = 1^4 + 3^4 + 4^4 + 4^4 + 7^4 + 7^4 + 10^4 = 1^4 + 3^4 + 5^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 9^4 + 9^4.

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

Cf. A345524, A345563, A345571, A345573, A345581, A345609, A345828.

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, 7):
    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])

A345580 Numbers that are the sum of eight fourth powers in five or more ways.

Original entry on oeis.org

4228, 4403, 4468, 5443, 5508, 5683, 6613, 6643, 6658, 6708, 6723, 6773, 6788, 6838, 6853, 6868, 6883, 6898, 6948, 6963, 7013, 7028, 7093, 7138, 7203, 7267, 7268, 7332, 7397, 7478, 7507, 7572, 7588, 7828, 7858, 7923, 7938, 7988, 8003, 8068, 8113, 8133, 8178

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			4403 is a term because 4403 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 8^4 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 8^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4.

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

Cf. A345535, A345571, A345579, A345581, A345589, A345613, A345837.

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 >= 5])
    for x in range(len(rets)):
        print(rets[x])

A345827 Numbers that are the sum of seven fourth powers in exactly five ways.

Original entry on oeis.org

6642, 6707, 6772, 6882, 6947, 7922, 7987, 8227, 8962, 9267, 9507, 9747, 10116, 10291, 10722, 10867, 10932, 10962, 11331, 11411, 11571, 12676, 12851, 12916, 13187, 13252, 13891, 13956, 14131, 14211, 14707, 14772, 14802, 14917, 14932, 14947, 15012, 15092, 15316

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345571 at term 16 because 10787 = 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 8^4 + 9^4 = 1^4 + 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 9^4 = 1^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 9^4 = 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 8^4 = 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 8^4.

			6707 is a term because 6707 = 1^4 + 1^4 + 1^4 + 2^4 + 6^4 + 6^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 = 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 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. A345571, A345777, A345817, A345826, A345828, A345837, A346282.

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

A345608 Numbers that are the sum of seven fifth powers in five or more ways.

Original entry on oeis.org

6768576, 6776120, 7883668, 8625376, 8740709, 10036201, 10604054, 12476826, 12618493, 13006575, 13060213, 13080706, 13174250, 13536416, 13550162, 13562501, 13662500, 14110656, 14583968, 15169276, 15247994, 16053313, 16060683, 16374218, 16573507, 16600001

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			6776120 is a term because 6776120 = 2^5 + 4^5 + 7^5 + 12^5 + 17^5 + 18^5 + 20^5 = 3^5 + 6^5 + 6^5 + 12^5 + 14^5 + 18^5 + 21^5 = 4^5 + 6^5 + 8^5 + 11^5 + 13^5 + 16^5 + 22^5 = 4^5 + 7^5 + 7^5 + 7^5 + 16^5 + 19^5 + 20^5 = 5^5 + 6^5 + 6^5 + 8^5 + 16^5 + 19^5 + 20^5.

Sean A. Irvine, Table of n, a(n) for n = 1..4721

Cf. A345571, A345607, A345609, A345613, A345719, A346282.

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

cp's OEIS Frontend

A345523 Numbers that are the sum of seven cubes in five or more ways.

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A345562 Numbers that are the sum of six fourth powers in five or more ways.

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A345570 Numbers that are the sum of seven fourth powers in four or more ways.

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A345572 Numbers that are the sum of seven fourth powers in six or more ways.

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A345580 Numbers that are the sum of eight fourth powers in five or more ways.

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A345827 Numbers that are the sum of seven fourth powers in exactly five ways.

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A345608 Numbers that are the sum of seven fifth powers in five or more ways.

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Python