A344942 -id:A344942 - cp's OEIS frontend

A344922 Numbers that are the sum of four fourth powers in seven or more ways.

6576339, 13155858, 16020018, 16408434, 22673634, 23056803, 26421474, 33734834, 35965458, 39786098, 39803778, 43583138, 51071619, 52652754, 53731458, 57976083, 63985314, 64365939, 67655779, 68846274, 73744563, 75951138, 77495778, 87038883, 88648914, 89148114

Offset: 1

David Consiglio, Jr., Jun 02 2021

nonn

			6576339 is a term because 6576339 = 1^4 + 24^4 + 41^4 + 43^4  = 3^4 + 7^4 + 41^4 + 44^4  = 4^4 + 23^4 + 27^4 + 49^4  = 6^4 + 31^4 + 41^4 + 41^4  = 7^4 + 11^4 + 36^4 + 47^4  = 7^4 + 21^4 + 28^4 + 49^4  = 12^4 + 17^4 + 29^4 + 49^4.

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Cf. A344729, A344904, A344923, A344924, A344942, A345150.

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

A344940 Numbers that are the sum of five fourth powers in six or more ways.

Original entry on oeis.org

151300, 197779, 211059, 217154, 225890, 236194, 236675, 243235, 246674, 250834, 286114, 288579, 300835, 302130, 302210, 303235, 309059, 317795, 320195, 334819, 334899, 335443, 336210, 338914, 346835, 356899, 363379, 366995, 373234, 375619, 389875, 391154

Offset: 1

David Consiglio, Jr., Jun 03 2021

nonn

			151300 is a term because 151300 = 3^4 + 3^4 + 3^4 + 12^4 + 19^4  = 3^4 + 11^4 + 11^4 + 14^4 + 17^4  = 3^4 + 13^4 + 13^4 + 13^4 + 16^4  = 6^4 + 9^4 + 9^4 + 9^4 + 19^4  = 7^4 + 11^4 + 11^4 + 11^4 + 18^4  = 8^4 + 9^4 + 13^4 + 13^4 + 17^4.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A344358, A344904, A344941, A344942, A345174, A345563, A345864.

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, 5):
    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])

A345180 Numbers that are the sum of five third powers in seven or more ways.

Original entry on oeis.org

4392, 4472, 4544, 4600, 4915, 4957, 5076, 5113, 5120, 5132, 5139, 5165, 5174, 5256, 5321, 5347, 5354, 5384, 5391, 5410, 5445, 5474, 5481, 5507, 5543, 5617, 5624, 5643, 5678, 5715, 5741, 5760, 5769, 5797, 5832, 5834, 5860, 5895, 5914, 5923, 5984, 5986, 6049

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

			4472 is a term because 4472 = 1^3 + 4^3 + 4^3 + 4^3 + 15^3  = 2^3 + 2^3 + 9^3 + 11^3 + 11^3  = 2^3 + 3^3 + 4^3 + 5^3 + 15^3  = 2^3 + 3^3 + 7^3 + 11^3 + 12^3  = 3^3 + 3^3 + 6^3 + 10^3 + 13^3  = 3^3 + 4^3 + 5^3 + 8^3 + 14^3  = 5^3 + 5^3 + 7^3 + 10^3 + 12^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A344800, A344942, A345150, A345174, A345181, A345183, A345516.

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

A345564 Numbers that are the sum of six fourth powers in seven or more ways.

Original entry on oeis.org

21251, 43875, 48276, 49796, 53315, 58035, 58500, 59780, 59795, 59811, 67875, 68306, 69155, 69779, 71955, 72051, 72131, 73970, 74420, 74851, 77010, 80291, 80515, 81875, 82275, 84515, 86436, 86451, 86531, 87075, 87746, 88355, 88595, 88660, 88675, 90355, 91475

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			43875 is a term because 43875 = 1^4 + 2^4 + 9^4 + 9^4 + 10^4 + 12^4 = 2^4 + 2^4 + 2^4 + 5^4 + 11^4 + 13^4 = 2^4 + 2^4 + 5^4 + 7^4 + 7^4 + 14^4 = 2^4 + 5^4 + 6^4 + 9^4 + 11^4 + 12^4 = 3^4 + 7^4 + 8^4 + 9^4 + 10^4 + 12^4 = 4^4 + 4^4 + 7^4 + 7^4 + 10^4 + 13^4 = 5^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4.

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

Cf. A344942, A345516, A345563, A345565, A345573, A345721, A345819.

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 >= 7])
    for x in range(len(rets)):
        print(rets[x])

A344943 Numbers that are the sum of five fourth powers in exactly seven ways.

Original entry on oeis.org

197779, 211059, 217154, 236675, 431155, 444019, 480739, 503539, 530659, 548994, 564979, 568450, 571539, 602450, 602770, 621859, 625635, 625939, 626194, 650659, 651954, 653059, 654130, 666739, 687314, 692754, 692899, 698019, 708499, 716739, 728914, 730914

Offset: 1

David Consiglio, Jr., Jun 03 2021

nonn

Differs from A344942 at term 10 because 534130 = 1^4 + 3^4 + 16^4 + 22^4 + 22^4 = 2^4 + 2^4 + 4^4 + 7^4 + 27^4 = 2^4 + 3^4 + 6^4 + 6^4 + 27^4 = 2^4 + 6^4 + 9^4 + 21^4 + 24^4 = 4^4 + 16^4 + 17^4 + 18^4 + 23^4 = 6^4 + 8^4 + 11^4 + 22^4 + 23^4 = 7^4 + 8^4 + 16^4 + 19^4 + 24^4 = 13^4 + 14^4 + 14^4 + 21^4 + 22^4.

			197779 is a term because 197779 = 1^4 + 5^4 + 6^4 + 16^4 + 19^4  = 1^4 + 7^4 + 11^4 + 12^4 + 20^4  = 1^4 + 10^4 + 12^4 + 17^4 + 17^4  = 2^4 + 4^4 + 5^4 + 7^4 + 21^4  = 3^4 + 5^4 + 6^4 + 6^4 + 21^4  = 4^4 + 7^4 + 9^4 + 13^4 + 20^4  = 11^4 + 13^4 + 14^4 + 15^4 + 16^4.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A344923, A344941, A344942, A344945, A345181, A345819.

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

A344944 Numbers that are the sum of five fourth powers in eight or more ways.

Original entry on oeis.org

534130, 619090, 654754, 663155, 729219, 737459, 742770, 758354, 775714, 810034, 813459, 816579, 831250, 906034, 930499, 954930, 954979, 1009954, 1055619, 1083955, 1099459, 1100579, 1101859, 1103554, 1106019, 1157634, 1167794, 1179379, 1180003, 1186834

Offset: 1

David Consiglio, Jr., Jun 03 2021

nonn

			534130 is a term because 534130 = 1^4 + 3^4 + 16^4 + 22^4 + 22^4  = 2^4 + 2^4 + 4^4 + 7^4 + 27^4  = 2^4 + 3^4 + 6^4 + 6^4 + 27^4  = 2^4 + 6^4 + 9^4 + 21^4 + 24^4  = 4^4 + 16^4 + 17^4 + 18^4 + 23^4  = 6^4 + 8^4 + 11^4 + 22^4 + 23^4  = 7^4 + 8^4 + 16^4 + 19^4 + 24^4  = 13^4 + 14^4 + 14^4 + 21^4 + 22^4.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A341891, A344922, A344924, A344942, A344945, A345183, A345565.

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, 5):
    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])

cp's OEIS Frontend

A344922 Numbers that are the sum of four fourth powers in seven or more ways.

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A344940 Numbers that are the sum of five fourth powers in six or more ways.

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A345180 Numbers that are the sum of five third powers in seven or more ways.

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A345564 Numbers that are the sum of six fourth powers in seven or more ways.

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A344943 Numbers that are the sum of five fourth powers in exactly seven ways.

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A344944 Numbers that are the sum of five fourth powers in eight or more ways.

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