A152442 n is included if the largest divisor of n that is coprime to d(n) is a composite, where d(n) is the number of divisors of n.

4, 15, 16, 21, 25, 27, 30, 33, 35, 36, 39, 42, 49, 50, 51, 54, 55, 57, 64, 65, 66, 69, 70, 75, 77, 78, 81, 85, 87, 91, 93, 95, 98, 100, 102, 105, 110, 111, 114, 115, 119, 120, 121, 123, 125, 129, 130, 133, 135, 138, 140, 141, 143, 144, 145, 147, 150, 154, 155, 159, 161

Offset: 1

Author

Leroy Quet, Dec 04 2008

Keywords

• nonn

Comments

A137926(a(n)) is composite for all n.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A137926, A152444.

Programs

Mathematica

a = {}; For[n = 2, n < 1000, n++, b = Max[Select[Divisors[n], GCD[DivisorSigma[0, n], # ] == 1 &]]; If[b > 1 && ! PrimeQ[b], AppendTo[a, n]]]; a (* Stefan Steinerberger, Dec 06 2008 *)
ldcQ[n_]:=CompositeQ[Max[Select[Divisors[n],CoprimeQ[#,DivisorSigma[0,n]]&]]]; Select[Range[200],ldcQ] (* Harvey P. Dale, Feb 19 2025 *)

Extensions

More terms from Stefan Steinerberger and Ray Chandler, Dec 06 2008