A152444 n is included if the largest proper divisor of n that is coprime to d(n) is a composite, where d(n) is the total number of divisors of n.

16, 27, 30, 36, 42, 50, 54, 64, 66, 70, 75, 78, 81, 98, 100, 102, 105, 110, 114, 120, 125, 130, 135, 138, 140, 144, 147, 150, 154, 162, 165, 168, 170, 174, 175, 182, 186, 189, 190, 195, 196, 200, 210, 216, 220, 222, 225, 230, 231, 238, 242, 245, 246, 250, 255

Offset: 1

Author

Leroy Quet, Dec 04 2008

Keywords

• nonn

Comments

A152443(a(n)) is composite for all n.

Examples

			There are 4 divisors of 27. These are 1,3,9,27. The proper divisors of 27 are therefore 1,3,9. The largest of these that is coprime to d(27) = 4 is 9. So a(27) = 9. (Note that in this case, the largest divisor of 27 coprime to 4 is 27, not 9.)
		

Crossrefs

Cf. A152442, A152443.

Programs

Mathematica

a = {}; For[n = 2, n < 1000, n++, b = Max[Select[Drop[Divisors[n], -1], GCD[DivisorSigma[0, n], # ] == 1 &]]; If[b > 1 && ! PrimeQ[b], AppendTo[a, n]]]; a (* Stefan Steinerberger, Dec 06 2008 *)

Extensions

Extended by Ray Chandler and Stefan Steinerberger, Dec 05 2008