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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) 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 August 30 17:11 EDT 2024. Contains 375545 sequences. (Running on oeis4.)