A345532 -id:A345532 - 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])

A345577 Numbers that are the sum of eight fourth powers in two or more ways.

Original entry on oeis.org

263, 278, 293, 308, 323, 343, 358, 373, 388, 423, 438, 453, 503, 518, 533, 548, 563, 583, 598, 613, 628, 678, 693, 758, 773, 788, 803, 853, 868, 887, 902, 917, 932, 933, 967, 982, 997, 1028, 1043, 1047, 1062, 1108, 1127, 1142, 1157, 1172, 1222, 1237, 1283

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			278 is a term because 278 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.

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

Cf. A003342, A345532, A345568, A345578, A345586, A345610, A345834.

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, 8):
    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])

A345520 Numbers that are the sum of seven cubes in two or more ways.

Original entry on oeis.org

131, 159, 166, 173, 185, 192, 211, 222, 229, 236, 243, 248, 255, 257, 262, 264, 269, 274, 276, 281, 283, 285, 288, 290, 292, 295, 299, 300, 302, 307, 309, 311, 314, 318, 320, 321, 325, 332, 333, 337, 339, 340, 344, 346, 348, 351, 353, 355, 358, 359, 360, 363

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			159 is a term because 159 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3.

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

Cf. A003330, A345479, A345511, A345521, A345532, A345568, A345774.

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, 7):
    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])

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])

A345784 Numbers that are the sum of eight cubes in exactly two ways.

Original entry on oeis.org

132, 139, 158, 160, 167, 174, 181, 186, 193, 195, 197, 200, 212, 216, 219, 238, 244, 251, 258, 265, 272, 277, 288, 296, 298, 300, 301, 303, 307, 314, 315, 317, 321, 322, 327, 328, 329, 333, 334, 336, 338, 340, 341, 348, 350, 352, 356, 359, 360, 361, 363, 366

Offset: 1

David Consiglio, Jr., Jun 26 2021

nonn

Differs from A345532 at term 16 because 223 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 6^3 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 4^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3 + 5^3.

Likely finite.

			139 is a term because 139 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 4^3 = 2^3 + 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..173

Cf. A345532, A345774, A345783, A345785, A345794, A345834.

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

A345489 Numbers that are the sum of eight squares in two or more ways.

Original entry on oeis.org

23, 26, 29, 31, 32, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 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

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			26 is a term because 26 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2 = 1^2 + 1^2 + 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. A345479, A345488, A345490, A345499, A345532.

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, 8):
    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])

cp's OEIS Frontend

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

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A345577 Numbers that are the sum of eight fourth powers in two or more ways.

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A345520 Numbers that are the sum of seven cubes in two 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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A345784 Numbers that are the sum of eight cubes in exactly two ways.

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A345489 Numbers that are the sum of eight squares in two or more ways.

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