A215567 Numbers k with the property that k and the k-th number which is a product of k primes have the largest prime divisor and with the same multiplicity.

3, 13, 20, 42, 44, 45, 56, 60, 86, 87, 112, 119, 121

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 16 2012

Keywords

• nonn
• less

Examples

			13 and the 13th 13-almost prime = 13*2^12 = 53248 have same largest prime factor = 13, with the same multiplicity, so 13 is a term.
		

Crossrefs

Cf. A001222, A101695, A215405.

Programs

Mathematica

AlmostPrimePi[k_Integer,n_]:=...;AlmostPrime[k_,n_]:=...;
fQ[n_]:=FactorInteger[n][[-1,1]]==FactorInteger[AlmostPrime[n,n]][[-1,1]];k=1;lst={};
While[k<150,If[fQ@k,AppendTo[lst,k];Print@k];k++];lst  (* Robert G. Wilson v, Aug 27 2012 *)

Extensions

a(9)-a(13) from Robert G. Wilson v, Aug 27 2012

Definition clarified by N. J. A. Sloane, Sep 04 2012