A345718 -id:A345718 - cp's OEIS frontend

A345561 Numbers that are the sum of six fourth powers in four or more ways.

6626, 6691, 6866, 9251, 9491, 10115, 10706, 10786, 11555, 12595, 14225, 14691, 14771, 15315, 15330, 15395, 15570, 16051, 16595, 16610, 16660, 16675, 16850, 17090, 17091, 17236, 17316, 17331, 17346, 17860, 17875, 17940, 17955, 18195, 18786, 18851, 18866, 19155

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			6691 is a term because 6691 = 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 = 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 = 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4.

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

Cf. A344354, A345513, A345560, A345562, A345570, A345718, A345816.

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

A344518 Numbers that are the sum of five positive fifth powers in four or more ways.

Original entry on oeis.org

287618651, 1386406515, 1763135232, 2494769760, 2619898293, 3096064443, 3291315732, 3749564512, 4045994624, 5142310350, 5183605813, 5658934676, 5880926107, 7205217018, 7401155424, 7691215599, 8429499101, 8926086432, 9006349824, 9051501568, 9203796832

Offset: 1

David Consiglio, Jr., May 21 2021

nonn

			287618651 is a term because
287618651 =  8^5 + 21^5 + 27^5 + 27^5 + 48^5
          =  9^5 + 13^5 + 26^5 + 37^5 + 46^5
          = 11^5 + 12^5 + 23^5 + 41^5 + 44^5
          = 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
[Corrected by _Patrick De Geest_, Dec 28 2024]

Sean A. Irvine, Table of n, a(n) for n = 1..4906

Cf. A342685, A342686, A342687, A342688, A342687, A344519, A345718, A345863, A345864, A346257.

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, 500)]
for pos in cwr(power_terms, 5):
    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])

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])

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])

A345719 Numbers that are the sum of six fifth powers in five or more ways.

Original entry on oeis.org

54827300, 74115800, 74883600, 75609125, 113088250, 120274275, 166078869, 169692136, 174781858, 178736448, 182341225, 185558208, 194939538, 203054589, 218814275, 235067008, 250989825, 251772882, 252721458, 255453233, 258124975, 274616694, 282859667

Offset: 1

David Consiglio, Jr., Jun 24 2021

nonn

			74115800 is a term because 74115800 = 1^5 + 4^5 + 21^5 + 21^5 + 29^5 + 34^5 = 1^5 + 8^5 + 14^5 + 23^5 + 32^5 + 32^5 = 4^5 + 11^5 + 13^5 + 22^5 + 24^5 + 36^5 = 5^5 + 6^5 + 19^5 + 20^5 + 24^5 + 36^5 = 6^5 + 25^5 + 25^5 + 25^5 + 29^5 + 30^5.

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

Cf. A345562, A345608, A345718, A345720, A345863, A346360.

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

A346359 Numbers that are the sum of six fifth powers in exactly four ways.

Original entry on oeis.org

12047994, 20646208, 21017489, 21300963, 21741819, 24993485, 27669050, 28576064, 30193856, 30785920, 35480456, 35735194, 36082750, 37303264, 39035975, 46814942, 47963291, 50047062, 50724345, 52987561, 53076800, 53606848, 55101101, 56766906, 57969327, 58125980

Offset: 1

David Consiglio, Jr., Jul 13 2021

nonn

Differs from A345718 at term 23 because 54827300 = 4^5 + 7^5 + 21^5 + 22^5 + 23^5 + 33^5 = 5^5 + 10^5 + 15^5 + 20^5 + 28^5 + 32^5 = 1^5 + 14^5 + 16^5 + 19^5 + 28^5 + 32^5 = 4^5 + 11^5 + 13^5 + 22^5 + 29^5 + 31^5 = 5^5 + 6^5 + 19^5 + 20^5 + 29^5 + 31^5.

			12047994 is a term because 12047994 = 7^5 + 9^5 + 12^5 + 14^5 + 17^5 + 25^5 = 5^5 + 10^5 + 13^5 + 15^5 + 16^5 + 25^5 = 1^5 + 1^5 + 3^5 + 4^5 + 21^5 + 24^5 = 4^5 + 6^5 + 15^5 + 15^5 + 21^5 + 23^5.

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

Cf. A344519, A345718, A345816, A346281, A346358, A346360.

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

cp's OEIS Frontend

A345561 Numbers that are the sum of six fourth powers in four or more ways.

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A344518 Numbers that are the sum of five positive fifth powers in four 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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A345607 Numbers that are the sum of seven fifth powers in four or more ways.

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A345719 Numbers that are the sum of six fifth powers in five or more ways.

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A346359 Numbers that are the sum of six fifth powers in exactly four ways.

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