A345564 -id:A345564 - cp's OEIS frontend

A345516 Numbers that are the sum of six cubes in seven or more ways.

1710, 1766, 1773, 1981, 1988, 2051, 2105, 2160, 2168, 2196, 2249, 2251, 2259, 2277, 2314, 2322, 2349, 2368, 2375, 2376, 2417, 2424, 2431, 2438, 2457, 2466, 2480, 2492, 2494, 2513, 2520, 2531, 2538, 2539, 2548, 2555, 2557, 2564, 2565, 2574, 2583, 2593, 2611

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			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..10000

Cf. A344811, A345180, A345515, A345517, A345525, A345564, A345769.

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])

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])

A345565 Numbers that are the sum of six fourth powers in eight or more ways.

Original entry on oeis.org

58035, 59780, 87746, 88595, 96195, 96450, 102371, 106451, 106515, 108035, 108275, 108290, 108771, 112370, 112931, 115251, 122835, 122850, 122915, 124691, 125971, 132546, 133395, 133571, 133586, 134675, 134931, 136931, 138275, 138595, 143650, 144755, 144835

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			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. A344944, A345517, A345564, A345566, A345574, A345722, A345820.

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])

A345573 Numbers that are the sum of seven fourth powers in seven or more ways.

Original entry on oeis.org

16691, 17347, 17971, 19491, 20706, 21252, 21267, 21332, 21507, 21636, 21876, 21956, 22547, 22612, 23156, 23587, 23652, 23827, 23892, 24436, 25107, 25347, 25427, 25716, 25971, 26051, 27812, 29092, 29187, 29332, 29427, 29442, 29636, 29701, 29716, 29956, 29971

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			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. A345525, A345564, A345572, A345574, A345582, A345629, A345829.

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])

A345819 Numbers that are the sum of six fourth powers in exactly seven ways.

Original entry on oeis.org

21251, 43875, 48276, 49796, 53315, 58500, 59795, 59811, 67875, 68306, 69155, 69779, 71955, 72051, 72131, 73970, 74420, 74851, 77010, 80291, 80515, 81875, 82275, 84515, 86436, 86451, 86531, 87075, 88355, 88660, 88675, 90355, 91475, 93410, 93650, 94690, 95155

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345564 at term 6 because 58035 = 1^4 + 1^4 + 9^4 + 10^4 + 12^4 + 12^4 = 1^4 + 4^4 + 5^4 + 8^4 + 11^4 + 14^4 = 1^4 + 5^4 + 6^4 + 11^4 + 12^4 + 12^4 = 2^4 + 2^4 + 4^4 + 5^4 + 13^4 + 13^4 = 2^4 + 6^4 + 6^4 + 7^4 + 7^4 + 15^4 = 2^4 + 8^4 + 10^4 + 11^4 + 11^4 + 11^4 = 3^4 + 4^4 + 4^4 + 4^4 + 9^4 + 15^4 = 4^4 + 5^4 + 6^4 + 9^4 + 12^4 + 13^4.

			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. A344943, A345564, A345769, A345818, A345820, A345829, A346362.

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])

A344942 Numbers that are the sum of five fourth powers in seven or more ways.

Original entry on oeis.org

197779, 211059, 217154, 236675, 431155, 444019, 480739, 503539, 530659, 534130, 548994, 564979, 568450, 571539, 602450, 602770, 619090, 621859, 625635, 625939, 626194, 650659, 651954, 653059, 654130, 654754, 663155, 666739, 687314, 692754, 692899, 698019

Offset: 1

David Consiglio, Jr., Jun 03 2021

nonn

			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. A344922, A344940, A344943, A344944, A345180, A345564.

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])

A345721 Numbers that are the sum of six fifth powers in seven or more ways.

Original entry on oeis.org

1184966816, 1700336000, 1717860100, 1972000800, 2229475325, 2295937600, 2396275200, 2548597632, 2625460992, 2886251808, 3217068800, 3697267200, 3729261536, 3765398725, 4046532448, 4165116967, 4246566632, 4286704224, 4335900525, 4489548050

Offset: 1

David Consiglio, Jr., Jun 24 2021

nonn

			1700336000 is a term because 1700336000 = 4^5 + 17^5 + 31^5 + 37^5 + 43^5 + 68^5 = 6^5 + 9^5 + 10^5 + 23^5 + 60^5 + 62^5 = 6^5 + 14^5 + 16^5 + 50^5 + 50^5 + 64^5 = 7^5 + 25^5 + 30^5 + 54^5 + 56^5 + 58^5 = 8^5 + 21^5 + 23^5 + 27^5 + 57^5 + 64^5 = 9^5 + 21^5 + 22^5 + 29^5 + 53^5 + 66^5 = 13^5 + 32^5 + 35^5 + 38^5 + 45^5 + 67^5.

Sean A. Irvine, Table of n, a(n) for n = 1..4091

Cf. A345564, A345629, A345720, A345722, A346362.

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])

cp's OEIS Frontend

A345516 Numbers that are the sum of six cubes in seven or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345565 Numbers that are the sum of six fourth powers in eight or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345573 Numbers that are the sum of seven fourth powers in seven or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345819 Numbers that are the sum of six fourth powers in exactly seven ways.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

A344942 Numbers that are the sum of five fourth powers in seven or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345721 Numbers that are the sum of six fifth powers in seven or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python