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).

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

Offset: 2

Author

M. Eren Kesim, Aug 25 2021

Keywords

• nonn
• tabl

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).

Examples

			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, ...
		

Links

• M. Eren Kesim, First Python program for A346460
• M. Eren Kesim, Second Python program for A346460

Crossrefs

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

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

Programs

Python

# See links.