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

1,1

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

Links

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

Example

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.

Mathematica

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

Crossrefs

Sequence in context: A163838 A228091 A157849 * A368715 A144976 A119622

Adjacent sequences: A137254 A137255 A137256 * A137258 A137259 A137260

Keyword

nonn

Author

Leroy Quet, Mar 11 2008

Extensions

More terms from Stefan Steinerberger, Mar 16 2008

Status

approved