A345606 -id:A345606 - cp's OEIS frontend

A345569 Numbers that are the sum of seven fourth powers in three or more ways.

2677, 2692, 2757, 2852, 2867, 2917, 2932, 2997, 3107, 3172, 3301, 3476, 3541, 3972, 4132, 4147, 4212, 4227, 4242, 4257, 4307, 4322, 4372, 4387, 4437, 4452, 4482, 4497, 4562, 4627, 4737, 4756, 4851, 4866, 4867, 4931, 4996, 5077, 5106, 5107, 5122, 5187, 5252

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			2692 is a term because 2692 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4.

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

Cf. A345521, A345560, A345568, A345570, A345578, A345606, A345825.

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 >= 3])
    for x in range(len(rets)):
        print(rets[x])

A345604 Numbers that are the sum of six fifth powers in three or more ways.

Original entry on oeis.org

696467, 893572, 1100264, 1109295, 1165727, 1711776, 2007401, 2025309, 2221767, 2801812, 3047519, 3310494, 3360608, 3550866, 3559556, 3576120, 3807122, 3907101, 4055922, 4093540, 4096114, 4104067, 4123363, 4135578, 4155107, 4195571, 4222339, 4326784, 4417112

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			893572 is a term because 893572 = 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 = 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 = 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 15^5.

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

Cf. A342687, A345507, A345560, A345606, A345718, A346358.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 3])
    for x in range(len(rets)):
        print(rets[x])

A345605 Numbers that are the sum of seven fifth powers in two or more ways.

Original entry on oeis.org

4099, 4130, 4161, 4341, 4372, 4583, 5122, 5153, 5364, 6145, 7223, 7254, 7465, 8246, 10347, 11874, 11905, 12116, 12897, 14998, 19649, 20905, 20936, 21147, 21928, 24029, 28680, 36866, 36897, 37108, 37711, 37889, 39990, 40138, 44641, 51393, 51448, 51479, 51510

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			4130 is a term because 4130 = 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 4^5 = 1^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5.

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

Cf. A003352, A345507, A345568, A345606, A345610, A346279.

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 >= 2])
    for x in range(len(rets)):
        print(rets[x])

A345607 Numbers that are the sum of seven fifth powers in four or more ways.

Original entry on oeis.org

893604, 1117071, 1182534, 1414559, 1629244, 1933328, 2280543, 2586035, 2867074, 3050644, 3055295, 3055977, 3256432, 3329360, 3369543, 3436058, 3551890, 3576363, 3896969, 3914877, 3930849, 4055954, 4087746, 4088690, 4093572, 4096665, 4098161, 4104068, 4104310

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			1117071 is a term because 1117071 = 1^5 + 2^5 + 6^5 + 7^5 + 7^5 + 14^5 + 14^5 = 2^5 + 2^5 + 4^5 + 6^5 + 10^5 + 12^5 + 15^5 = 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 7^5 + 16^5 = 3^5 + 5^5 + 6^5 + 6^5 + 7^5 + 8^5 + 16^5.

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

Cf. A345570, A345606, A345608, A345612, A345718, A346281.

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 >= 4])
    for x in range(len(rets)):
        print(rets[x])

A345611 Numbers that are the sum of eight fifth powers in three or more ways.

Original entry on oeis.org

52417, 54518, 69634, 70954, 84458, 84489, 84700, 85481, 87582, 92233, 101264, 102890, 112574, 117225, 119326, 134473, 143264, 143442, 143506, 149781, 151448, 158719, 159465, 165634, 166998, 167029, 167196, 167240, 168021, 170122, 174773, 183804, 184457

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			54518 is a term because 54518 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 7^5 = 1^5 + 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 8^5 = 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 7^5 + 7^5 + 7^5.

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

Cf. A345578, A345606, A345610, A345612, A345620, A346328.

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, 8):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 3])
    for x in range(len(rets)):
        print(rets[x])

A346280 Numbers that are the sum of seven fifth powers in exactly three ways.

Original entry on oeis.org

84457, 166997, 324860, 326199, 358482, 359327, 391007, 391999, 408158, 455146, 455749, 486468, 502429, 572054, 595519, 614505, 622280, 648319, 671210, 672022, 696468, 696499, 696710, 697491, 699592, 704243, 713274, 729235, 755516, 796467, 857518, 877645

Offset: 1

David Consiglio, Jr., Jul 13 2021

nonn

Differs from A345606 at term 39 because 893604 = 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 10^5 + 15^5 = 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 15^5 = 2^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 = 2^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5.

			84457 is a term because 84457 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 9^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 = 1^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 8^5.

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

Cf. A345606, A345825, A346279, A346281, A346328, A346358.

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 == 3])
    for x in range(len(rets)):
        print(rets[x])

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A345569 Numbers that are the sum of seven fourth powers in three or more ways.

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A345604 Numbers that are the sum of six fifth powers in three or more ways.

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A345605 Numbers that are the sum of seven fifth powers in two or more ways.

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A345607 Numbers that are the sum of seven fifth powers in four or more ways.

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Python

A345611 Numbers that are the sum of eight fifth powers in three or more ways.

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Python

A346280 Numbers that are the sum of seven fifth powers in exactly three ways.

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Python