A345542 -id:A345542 - cp's OEIS frontend

A345533 Numbers that are the sum of eight cubes in three or more ways.

223, 230, 237, 249, 256, 263, 270, 275, 282, 284, 286, 289, 291, 293, 308, 310, 312, 319, 326, 345, 347, 349, 354, 364, 371, 373, 375, 378, 380, 382, 385, 386, 387, 389, 397, 399, 401, 404, 406, 408, 410, 412, 413, 415, 420, 423, 427, 434, 438, 439, 441, 443

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			230 is a term because 230 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 5^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 = 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. A345490, A345521, A345532, A345534, A345542, A345578, A345785.

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 >= 3])
    for x in range(len(rets)):
        print(rets[x])

A345543 Numbers that are the sum of nine cubes in four or more ways.

Original entry on oeis.org

224, 257, 264, 283, 320, 348, 355, 372, 374, 376, 381, 383, 390, 400, 402, 407, 409, 411, 413, 414, 416, 428, 435, 439, 442, 446, 450, 453, 454, 461, 465, 472, 474, 476, 479, 481, 486, 488, 491, 498, 500, 502, 503, 505, 507, 509, 510, 512, 514, 517, 519, 524

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			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..10000

Cf. A345501, A345534, A345542, A345544, A345552, A345588, A345796.

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])

A345587 Numbers that are the sum of nine fourth powers in three or more ways.

Original entry on oeis.org

519, 534, 599, 774, 1143, 1364, 1539, 1604, 1619, 1814, 2579, 2644, 2659, 2679, 2694, 2709, 2724, 2739, 2754, 2759, 2774, 2789, 2819, 2834, 2839, 2854, 2869, 2884, 2899, 2919, 2934, 2949, 2964, 2994, 2999, 3014, 3029, 3079, 3094, 3109, 3124, 3139, 3159, 3174

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			534 is a term because 534 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4.

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

Cf. A345542, A345578, A345586, A345588, A345596, A345620, A345845.

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 >= 3])
    for x in range(len(rets)):
        print(rets[x])

A345541 Numbers that are the sum of nine cubes in two or more ways.

Original entry on oeis.org

72, 133, 140, 147, 159, 161, 166, 168, 175, 182, 185, 187, 189, 194, 196, 198, 201, 203, 205, 208, 213, 217, 220, 222, 224, 227, 231, 238, 239, 243, 245, 246, 250, 252, 257, 259, 261, 264, 265, 266, 271, 273, 276, 278, 280, 283, 285, 287, 289, 290, 292, 294

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			133 is a term because 133 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3.

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

Cf. A003332, A345499, A345532, A345542, A345550, A345586, A345794.

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 >= 2])
    for x in range(len(rets)):
        print(rets[x])

A345551 Numbers that are the sum of ten cubes in three or more ways.

Original entry on oeis.org

197, 225, 232, 239, 246, 251, 253, 258, 260, 265, 267, 272, 277, 279, 281, 284, 286, 288, 291, 293, 295, 298, 300, 302, 303, 305, 307, 309, 310, 312, 314, 316, 317, 319, 321, 323, 324, 326, 328, 329, 330, 335, 336, 338, 340, 342, 343, 344, 345, 347, 349, 351

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			225 is a term because 225 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 5^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 = 1^3 + 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. A345510, A345542, A345550, A345552, A345596, A345805.

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 >= 3])
    for x in range(len(rets)):
        print(rets[x])

A345795 Numbers that are the sum of nine cubes in exactly three ways.

Original entry on oeis.org

231, 238, 245, 250, 259, 271, 276, 278, 280, 285, 287, 290, 292, 294, 297, 299, 301, 302, 309, 311, 313, 315, 316, 318, 322, 327, 334, 335, 337, 339, 341, 346, 350, 353, 357, 362, 365, 379, 386, 387, 388, 391, 393, 394, 395, 397, 398, 405, 412, 418, 420, 421

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345542 at term 1 because 224 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 6^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3 = 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.

Likely finite.

			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..136

Cf. A345542, A345785, A345794, A345796, A345805, A345845.

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])

A345500 Numbers that are the sum of nine squares in three or more ways.

Original entry on oeis.org

33, 36, 39, 41, 42, 44, 45, 47, 48, 49, 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

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. A345490, A345499, A345501, A345510, A345542.

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 >= 3])
    for x in range(len(rets)):
        print(rets[x])

cp's OEIS Frontend

A345533 Numbers that are the sum of eight cubes in three or more ways.

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A345543 Numbers that are the sum of nine cubes in four or more ways.

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A345587 Numbers that are the sum of nine fourth powers in three or more ways.

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A345541 Numbers that are the sum of nine cubes in two or more ways.

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A345551 Numbers that are the sum of ten cubes in three or more ways.

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A345795 Numbers that are the sum of nine cubes in exactly three ways.

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A345500 Numbers that are the sum of nine squares in three or more ways.

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Python