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A346460 Square array read by downward antidiagonals in which row n lists all numbers k for which all positive integers cannot be colored with two colors without any positive integer x being the same color as n*x or k*x (for n >= 2). 3
4, 16, 9, 64, 81, 2, 256, 729, 8, 25, 1024, 6561, 16, 625, 36, 4096, 59049, 32, 15625, 1296, 49, 16384, 531441, 128, 390625, 46656, 2401, 4, 65536, 4782969, 256, 9765625, 1679616, 117649, 16, 3, 262144, 43046721, 512, 244140625, 60466176, 5764801, 64, 27, 100 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Row n lists all positive integers k for which there exists at least one pair of positive integers (x, y) such that n^x = k^y and x+y is odd.

If n is an element of A007916, then row n lists all perfect powers of n^2.

A positive integer k is in row n if and only if there exists a positive integer x for which A052410(n)^x = k and A007814(A052409(n)) != A007814(x).

LINKS

Table of n, a(n) for n=2..46.

M. Eren Kesim, First Python program for A346460

M. Eren Kesim, Second Python program for A346460

EXAMPLE

Table begins:

     4,    16,      64,       256,        1024,          4096,           16384, ...

     9,    81,     729,      6561,       59049,        531441,         4782969, ...

     2,     8,      16,        32,         128,           256,             512, ...

    25,   625,   15625,    390625,     9765625,     244140625,      6103515625, ...

    36,  1296,   46656,   1679616,    60466176,    2176782336,      7836416409, ...

    49,  2401,  117649,   5764801,   282475249,   13841287201,    678223072849, ...

     4,    16,      64,       256,        1024,          4096,           16384, ...

     3,    27,      81,       243,        2187,          6561,           19683, ...

   100, 10000, 1000000, 100000000, 10000000000, 1000000000000, 100000000000000, ...

PROG

(Python) See links.

CROSSREFS

First few rows are A000302, A001019, A346461, A009969, A009980, and A087752.

Cf. A007814, A007916, A013708-A013715, A052409, A052410, A098608, A346459.

Sequence in context: A337340 A061093 A067178 * A181717 A224173 A223864

Adjacent sequences:  A346457 A346458 A346459 * A346461 A346462 A346463

KEYWORD

nonn,tabl

AUTHOR

M. Eren Kesim, Aug 25 2021

STATUS

approved

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Last modified January 23 17:33 EST 2022. Contains 350514 sequences. (Running on oeis4.)