A345562 -id:A345562 - cp's OEIS frontend

A344358 Numbers that are the sum of five fourth powers in five or more ways.

59779, 67859, 93394, 108274, 112850, 136915, 142354, 151300, 151475, 161459, 168979, 181219, 183539, 183604, 185299, 187699, 189394, 193379, 195394, 197779, 199090, 199474, 200979, 201874, 202979, 203299, 205859, 211059, 211330, 212419, 213730, 217154, 217810, 217890, 221779, 223090, 223155

Offset: 1

David Consiglio, Jr., May 15 2021

nonn

			93394 is a term of this sequence because 93394 = 1^4 + 4^4 + 8^4 + 14^4 + 15^4 = 1^4 + 6^4 + 12^4 + 12^4 + 15^4 = 1^4 + 9^4 + 10^4 + 14^4 + 14^4 = 5^4 + 6^4 + 11^4 + 14^4 + 14^4 = 5^4 + 7^4 + 8^4 + 12^4 + 16^4.

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Cf. A343989, A344354, A344356, A344359, A344940, A345562, A345863.

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, 50)]
for pos in cwr(power_terms, 5):
    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])

A345514 Numbers that are the sum of six cubes in five or more ways.

Original entry on oeis.org

1045, 1169, 1241, 1260, 1377, 1384, 1432, 1440, 1488, 1495, 1530, 1539, 1549, 1556, 1558, 1584, 1586, 1594, 1595, 1602, 1612, 1617, 1640, 1647, 1654, 1657, 1673, 1675, 1677, 1703, 1710, 1712, 1715, 1719, 1729, 1736, 1738, 1745, 1747, 1754, 1764, 1766, 1771

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			1169 is a term because 1169 = 1^3 + 2^3 + 2^3 + 3^3 + 4^3 + 9^3 = 1^3 + 2^3 + 5^3 + 5^3 + 5^3 + 7^3 = 1^3 + 3^3 + 4^3 + 4^3 + 4^3 + 8^3 = 2^3 + 3^3 + 3^3 + 4^3 + 5^3 + 8^3 = 3^3 + 3^3 + 3^3 + 3^3 + 7^3 + 7^3.

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

Cf. A343989, A344809, A345513, A345515, A345523, A345562, A345767.

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

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

Original entry on oeis.org

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])

A345563 Numbers that are the sum of six fourth powers in six or more ways.

Original entry on oeis.org

21251, 37811, 38051, 43251, 43571, 43875, 44115, 44531, 45155, 45651, 45891, 47411, 47586, 48276, 49796, 49971, 52195, 53235, 53315, 54131, 56290, 57395, 57460, 57570, 58035, 58500, 59075, 59330, 59780, 59795, 59811, 59860, 60035, 62180, 62211, 63971, 66340

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			37811 is a term because 37811 = 1^4 + 2^4 + 2^4 + 7^4 + 11^4 + 12^4 = 2^4 + 2^4 + 4^4 + 7^4 + 9^4 + 13^4 = 2^4 + 3^4 + 6^4 + 6^4 + 9^4 + 13^4 = 3^4 + 4^4 + 8^4 + 8^4 + 11^4 + 11^4 = 4^4 + 6^4 + 7^4 + 9^4 + 9^4 + 12^4 = 5^4 + 5^4 + 9^4 + 10^4 + 10^4 + 10^4.

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

Cf. A344940, A345515, A345562, A345564, A345572, A345720, A345818.

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 >= 6])
    for x in range(len(rets)):
        print(rets[x])

A345571 Numbers that are the sum of seven fourth powers in five or more ways.

Original entry on oeis.org

6642, 6707, 6772, 6882, 6947, 7922, 7987, 8227, 8962, 9267, 9507, 9747, 10116, 10291, 10722, 10787, 10867, 10932, 10962, 11331, 11411, 11571, 12676, 12851, 12916, 13187, 13252, 13891, 13956, 14131, 14211, 14707, 14772, 14802, 14917, 14932, 14947, 15012, 15092

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			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. A345523, A345562, A345570, A345572, A345580, A345608, A345827.

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])

A345817 Numbers that are the sum of six fourth powers in exactly five ways.

Original entry on oeis.org

15395, 16610, 18866, 19235, 19410, 20996, 21011, 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, 37971, 38595, 38675, 39266, 39890

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345562 at term 8 because 21251 = 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 12^4 = 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 11^4 = 1^4 + 7^4 + 8^4 + 8^4 + 8^4 + 9^4 = 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 11^4 = 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 12^4 = 2^4 + 4^4 + 6^4 + 9^4 + 9^4 + 9^4 = 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 11^4.

			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. A344359, A345562, A345767, A345816, A345818, A345827, A346360.

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])

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])

cp's OEIS Frontend

A344358 Numbers that are the sum of five fourth powers in five or more ways.

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A345514 Numbers that are the sum of six cubes in five or more ways.

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

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A345563 Numbers that are the sum of six fourth powers in six or more ways.

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A345571 Numbers that are the sum of seven fourth powers in five or more ways.

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A345817 Numbers that are the sum of six fourth powers in exactly five ways.

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

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