A137257 A number k is included if there is at least one (nonzero) exponent in the prime factorization of k that is not coprime to k.

4, 12, 16, 18, 20, 24, 27, 28, 36, 44, 48, 50, 52, 54, 60, 64, 68, 72, 76, 80, 84, 90, 92, 98, 100, 108, 112, 116, 120, 124, 126, 132, 135, 140, 144, 148, 150, 156, 160, 162, 164, 168, 172, 176, 180, 188, 189, 192, 196, 198, 200, 204, 208, 212, 216, 220, 228, 234

Offset: 1

Author

Leroy Quet, Mar 11 2008

Keywords

• nonn

Comments

The number of terms not exceeding 10^m, for m = 1, 2, ..., are 1, 25, 254, 2567, 25730, 257286, 2572950, 25729433, 257294360, 2572944786, ... . Apparently, the asymptotic density of this sequence exists and equals 0.257294... . - Amiram Eldar, Jun 24 2022

Examples

			48 = 2^4 * 3^1; so the exponents in the prime factorization of 48 are 4 and 1. 48 is not coprime to 4; therefore 48 is included in this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Select[Range[3000], GCD[ #, Product[FactorInteger[ # ][[i, 2]], {i, 1, Length[FactorInteger[ # ]]}]] > 1 &] (* Stefan Steinerberger, Mar 16 2008 *)

Extensions

More terms from Stefan Steinerberger, Mar 16 2008