A376279 -id:A376279 - cp's OEIS frontend

A376291 Numbers k such that k^k is not a cube and can be expressed as (a^3 + b^3)/2 for positive integers a, b.

76, 112, 172, 364, 427, 532

Offset: 1

Chai Wah Wu, Sep 19 2024

Sequence is equal to all terms in A267415 that are not in A376279.

If a or b are allowed to be 0, then 2, 4, 128, 256, 686, 1372, 2000, 4000, 4394, ... are also terms.

			76^76 is not a cube and is equal to (523974089123227128080087214816032969930445946880^3 + 314384453473936276848052328889619781958267568128^3)/2.
112^112 is not a cube and is equal to (39739105680019344543609706294181022974041418385894471812303329593638887882752^3 + 13246368560006448181203235431393674324680472795298157270767776531212962627584^3)/2.
172^172 is not a cube and is equal to (186302856478727791003189416646781404088735216286873615701287403506960347135763572314025783484358072432973760558663310530664464384^3 + 26614693782675398714741345235254486298390745183839087957326771929565763876537653187717969069194010347567680079809044361523494912^3)/2

Cf. A267415, A376279.

A376315 Positive numbers k such that 2*k^k is a cube.

Original entry on oeis.org

2, 4, 128, 256, 686, 1372, 2000, 4000, 4394, 8192, 8788, 13718, 16384, 21296, 27436, 31250, 42592, 43904, 59582, 62500, 78608, 87808, 101306, 119164, 128000, 157216, 159014, 194672, 202612, 235298, 256000, 281216, 318028, 332750, 389344, 390224, 453962, 470596

Offset: 1

Chai Wah Wu, Sep 20 2024

nonn

{a(n)} UNION A376291 = positive numbers k such that k^k is not a cube and can be expressed as (x^3 + y^3)/2 for nonnegative integers x, y.

All terms are even.

Chai Wah Wu, Table of n, a(n) for n = 1..897

Cf. A376291, A376279.

from itertools import count, islice
from sympy import factorint
def A376315_gen(startvalue=2): # generator of terms >= startvalue
    for k in count(max(startvalue+(startvalue&1),2),2):
        f = {p:k*e for p,e in factorint(k).items()}
        f[2] += 1
        if not any(v%3 for v in f.values()):
            yield k
A376315_list = list(islice(A376315_gen(),30))

cp's OEIS Frontend

A376291 Numbers k such that k^k is not a cube and can be expressed as (a^3 + b^3)/2 for positive integers a, b.

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A376315 Positive numbers k such that 2*k^k is a cube.

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