A345543 -id:A345543 - cp's OEIS frontend

A345534 Numbers that are the sum of eight cubes in four or more ways.

256, 347, 382, 401, 408, 427, 434, 438, 445, 464, 471, 478, 480, 490, 497, 499, 502, 504, 506, 511, 516, 523, 530, 532, 534, 537, 560, 565, 567, 569, 571, 578, 586, 593, 595, 597, 600, 602, 604, 605, 611, 612, 616, 619, 621, 623, 624, 626, 628, 630, 635, 642

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			347 is a term because 347 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 5^3 = 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 + 4^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 5^3.

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

Cf. A345491, A345522, A345533, A345535, A345543, A345579, A345786.

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, 8):
    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])

A345542 Numbers that are the sum of nine positive cubes in three or more ways.

Original entry on oeis.org

224, 231, 238, 245, 250, 257, 259, 264, 271, 276, 278, 280, 283, 285, 287, 290, 292, 294, 297, 299, 301, 302, 309, 311, 313, 315, 316, 318, 320, 322, 327, 334, 335, 337, 339, 341, 346, 348, 350, 353, 355, 357, 362, 365, 372, 374, 376, 379, 381, 383, 386, 387

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			231 is a term because 231 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 5^3 = 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3.

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

Cf. A345500, A345533, A345541, A345543, A345551, A345587, A345795.

Select[Range[400],Length[Select[PowersRepresentations[#,9,3],FreeQ[ #,0]&]]> 2&] (* Harvey P. Dale, Jan 04 2022 *)

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, 9):
    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])

Definition corrected by Harvey P. Dale, Jan 04 2022

A345544 Numbers that are the sum of nine cubes in five or more ways.

Original entry on oeis.org

409, 413, 428, 435, 439, 446, 465, 472, 479, 491, 498, 502, 505, 507, 512, 517, 524, 526, 531, 533, 535, 538, 540, 559, 561, 563, 566, 568, 570, 576, 579, 580, 587, 594, 596, 598, 600, 601, 603, 605, 613, 615, 617, 620, 622, 624, 627, 629, 631, 632, 633, 635

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			413 is a term because 413 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 5^3 = 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 = 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 5^3.

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

Cf. A345502, A345535, A345543, A345545, A345553, A345589, A345797.

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, 9):
    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])

A345588 Numbers that are the sum of nine fourth powers in four or more ways.

Original entry on oeis.org

2854, 2919, 2934, 2949, 2964, 3014, 3029, 3094, 3159, 3174, 3189, 3204, 3254, 3269, 3429, 3444, 3558, 3573, 3638, 3798, 3813, 3974, 4034, 4134, 4149, 4164, 4179, 4182, 4209, 4214, 4229, 4244, 4274, 4294, 4309, 4374, 4389, 4404, 4419, 4439, 4454, 4469, 4484

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			2919 is a term because 2919 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4.

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

Cf. A345543, A345579, A345587, A345589, A345597, A345621, A345846.

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, 9):
    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])

A345796 Numbers that are the sum of nine cubes in exactly four ways.

Original entry on oeis.org

224, 257, 264, 283, 320, 348, 355, 372, 374, 376, 381, 383, 390, 400, 402, 407, 411, 414, 416, 442, 450, 453, 454, 461, 474, 476, 481, 486, 488, 500, 503, 509, 510, 514, 519, 528, 529, 537, 542, 543, 544, 545, 548, 550, 552, 554, 555, 557, 564, 572, 573, 574

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345543 at term 17 because 409 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 5^3 + 5^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 4^3 + 4^3 + 6^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 5^3 + 5^3 + 5^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 5^3 + 6^3 = 2^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3.

Likely finite.

			257 is a term because 257 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 4^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 5^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 4^3.

Sean A. Irvine, Table of n, a(n) for n = 1..124

Cf. A345543, A345786, A345795, A345797, A345806, A345846.

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, 9):
    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])

A345552 Numbers that are the sum of ten cubes in four or more ways.

Original entry on oeis.org

225, 232, 251, 258, 265, 272, 284, 286, 288, 291, 307, 310, 314, 321, 323, 328, 342, 347, 349, 356, 363, 366, 373, 375, 377, 380, 382, 384, 389, 391, 398, 399, 401, 403, 405, 408, 410, 412, 414, 415, 417, 419, 421, 422, 424, 427, 429, 434, 436, 438, 440, 441

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			232 is a term because 232 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 5^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 = 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.

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

Cf. A345543, A345551, A345553, A345597, A345806.

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, 10):
    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])

A345501 Numbers that are the sum of nine squares in four or more ways.

Original entry on oeis.org

33, 36, 39, 41, 42, 44, 45, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			36 is a term because 36 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 5^2 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2 = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2.

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Cf. A345491, A345500, A345502, A345543.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 9):
    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

A345534 Numbers that are the sum of eight cubes in four or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345542 Numbers that are the sum of nine positive cubes in three or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Python

Extensions

A345544 Numbers that are the sum of nine cubes in five or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345588 Numbers that are the sum of nine fourth powers in four or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345796 Numbers that are the sum of nine cubes in exactly four ways.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

A345552 Numbers that are the sum of ten cubes in four or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345501 Numbers that are the sum of nine squares in four or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python