A345819 -id:A345819 - cp's OEIS frontend

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

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])

A345818 Numbers that are the sum of six fourth powers in exactly six ways.

Original entry on oeis.org

37811, 38051, 43251, 43571, 44115, 44531, 45155, 45651, 45891, 47411, 47586, 49971, 52195, 53235, 54131, 56290, 57395, 57460, 57570, 59075, 59330, 59860, 60035, 62180, 62211, 63971, 66340, 67026, 67635, 67715, 67860, 67940, 68115, 68291, 68484, 69395, 69410

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345563 at term 1 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.

			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. A344941, A345563, A345768, A345817, A345819, A345828, A346361.

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])

A345820 Numbers that are the sum of six fourth powers in exactly eight ways.

Original entry on oeis.org

58035, 59780, 87746, 96195, 96450, 102371, 106451, 106515, 108035, 108275, 108290, 108771, 112370, 112931, 115251, 122835, 122850, 124691, 125971, 133395, 133571, 133586, 134675, 136931, 138275, 138595, 143650, 144755, 145826, 147491, 148820, 149571, 150115

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345565 at term 4 because 88595 = 1^4 + 4^4 + 5^4 + 12^4 + 13^4 + 14^4 = 1^4 + 6^4 + 6^4 + 11^4 + 12^4 + 15^4 = 1^4 + 7^4 + 8^4 + 9^4 + 10^4 + 16^4 = 2^4 + 8^4 + 9^4 + 9^4 + 12^4 + 15^4 = 2^4 + 10^4 + 11^4 + 11^4 + 12^4 + 13^4 = 4^4 + 6^4 + 6^4 + 9^4 + 13^4 + 15^4 = 5^4 + 6^4 + 7^4 + 8^4 + 11^4 + 16^4 = 7^4 + 7^4 + 10^4 + 11^4 + 12^4 + 14^4.

			59780 is a term because 59780 = 1^4 + 1^4 + 1^4 + 5^4 + 12^4 + 14^4 = 1^4 + 1^4 + 6^4 + 6^4 + 9^4 + 15^4 = 1^4 + 2^4 + 9^4 + 10^4 + 11^4 + 13^4 = 1^4 + 4^4 + 7^4 + 7^4 + 8^4 + 15^4 = 1^4 + 7^4 + 7^4 + 9^4 + 10^4 + 14^4 = 2^4 + 5^4 + 6^4 + 11^4 + 11^4 + 13^4 = 3^4 + 7^4 + 8^4 + 10^4 + 11^4 + 13^4 = 5^4 + 6^4 + 7^4 + 7^4 + 11^4 + 14^4.

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

Cf. A344945, A345565, A345770, A345819, A345821, A345830, A346363.

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 == 8])
    for x in range(len(rets)):
        print(rets[x])

A345829 Numbers that are the sum of seven fourth powers in exactly seven ways.

Original entry on oeis.org

16691, 17347, 17971, 20706, 21956, 22547, 22612, 23156, 23587, 23827, 23892, 24436, 25107, 25427, 25716, 25971, 26051, 27812, 29092, 29187, 29332, 29427, 29442, 29636, 29701, 29716, 29956, 29971, 30036, 30132, 30612, 30981, 30996, 31011, 31316, 31331, 31347

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345573 at term 4 because 19491 = 1^4 + 1^4 + 1^4 + 6^4 + 8^4 + 8^4 + 10^4 = 1^4 + 2^4 + 4^4 + 4^4 + 7^4 + 9^4 + 10^4 = 1^4 + 2^4 + 5^4 + 8^4 + 8^4 + 8^4 + 9^4 = 1^4 + 3^4 + 4^4 + 6^4 + 6^4 + 9^4 + 10^4 = 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 8^4 + 11^4 = 2^4 + 4^4 + 4^4 + 5^4 + 6^4 + 7^4 + 11^4 = 3^4 + 4^4 + 4^4 + 7^4 + 7^4 + 8^4 + 10^4 = 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 6^4 + 11^4 = 3^4 + 5^4 + 7^4 + 8^4 + 8^4 + 8^4 + 8^4.

			17347 is a term because 17347 = 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 11^4 = 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 11^4 = 1^4 + 4^4 + 7^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 2^4 + 2^4 + 3^4 + 8^4 + 9^4 + 9^4 = 2^4 + 4^4 + 4^4 + 6^4 + 7^4 + 9^4 + 9^4 = 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 9^4 + 9^4.

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

Cf. A345573, A345779, A345819, A345828, A345830, A345839, A346284.

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 == 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])

A345769 Numbers that are the sum of six cubes in exactly seven ways.

Original entry on oeis.org

1710, 1766, 1773, 1988, 2051, 2160, 2196, 2249, 2251, 2259, 2314, 2322, 2349, 2375, 2417, 2424, 2480, 2492, 2513, 2520, 2531, 2539, 2548, 2564, 2565, 2574, 2611, 2613, 2639, 2656, 2702, 2707, 2762, 2770, 2773, 2792, 2798, 2808, 2818, 2825, 2826, 2833, 2844

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345516 at term 4 because 1981 = 1^3 + 1^3 + 1^3 + 5^3 + 5^3 + 12^3 = 1^3 + 1^3 + 2^3 + 3^3 + 6^3 + 12^3 = 1^3 + 1^3 + 5^3 + 5^3 + 9^3 + 10^3 = 1^3 + 1^3 + 6^3 + 6^3 + 6^3 + 11^3 = 1^3 + 2^3 + 3^3 + 6^3 + 9^3 + 10^3 = 3^3 + 3^3 + 7^3 + 7^3 + 8^3 + 9^3 = 3^3 + 4^3 + 6^3 + 6^3 + 9^3 + 9^3 = 4^3 + 4^3 + 5^3 + 6^3 + 8^3 + 10^3.

			1766 is a term because 1766 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 11^3 = 1^3 + 1^3 + 1^3 + 5^3 + 5^3 + 10^3 = 1^3 + 1^3 + 2^3 + 3^3 + 8^3 + 9^3 = 1^3 + 3^3 + 3^3 + 5^3 + 8^3 + 8^3 = 1^3 + 3^3 + 3^3 + 4^3 + 7^3 + 9^3 = 2^3 + 2^3 + 3^3 + 6^3 + 6^3 + 9^3 = 3^3 + 3^3 + 3^3 + 3^3 + 5^3 + 10^3.

Sean A. Irvine, Table of n, a(n) for n = 1..1359

Cf. A345181, A345516, A345768, A345770, A345779, A345819.

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

A346362 Numbers that are the sum of six fifth powers in exactly seven ways.

Original entry on oeis.org

1184966816, 1700336000, 1717860100, 1972000800, 2229475325, 2396275200, 2548597632, 2625460992, 2886251808, 3217068800, 3697267200, 3729261536, 3765398725, 4046532448, 4165116967, 4246566632, 4286704224, 4489548050, 4539955200, 4623694108, 4710031469

Offset: 1

David Consiglio, Jr., Jul 13 2021

nonn

Differs from A345721 at term 6 because 2295937600 = 4^5 + 21^5 + 38^5 + 42^5 + 43^5 + 72^5 = 8^5 + 16^5 + 30^5 + 42^5 + 54^5 + 70^5 = 8^5 + 13^5 + 36^5 + 37^5 + 57^5 + 69^5 = 14^5 + 16^5 + 16^5 + 52^5 + 54^5 + 68^5 = 3^5 + 14^5 + 32^5 + 44^5 + 61^5 + 66^5 = 4^5 + 18^5 + 22^5 + 52^5 + 58^5 + 66^5 = 10^5 + 14^5 + 26^5 + 42^5 + 63^5 + 65^5 = 1^5 + 7^5 + 34^5 + 57^5 + 58^5 + 63^5.

			1184966816 is a term because 1184966816 = 15^5 + 24^5 + 27^5 + 38^5 + 39^5 + 63^5 = 2^5 + 28^5 + 36^5 + 36^5 + 42^5 + 62^5 = 4^5 + 24^5 + 38^5 + 38^5 + 40^5 + 62^5 = 21^5 + 32^5 + 37^5 + 41^5 + 45^5 + 60^5 = 8^5 + 14^5 + 34^5 + 40^5 + 52^5 + 58^5 = 11^5 + 17^5 + 22^5 + 49^5 + 51^5 + 56^5 = 11^5 + 16^5 + 22^5 + 52^5 + 52^5 + 53^5.

Sean A. Irvine, Table of n, a(n) for n = 1..2648

Cf. A345721, A345819, A346284, A346361, A346363.

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

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

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A345818 Numbers that are the sum of six fourth powers in exactly six ways.

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A345820 Numbers that are the sum of six fourth powers in exactly eight ways.

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A345829 Numbers that are the sum of seven fourth powers in exactly seven ways.

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

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A345769 Numbers that are the sum of six cubes in exactly seven ways.

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A346362 Numbers that are the sum of six fifth powers in exactly seven ways.

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