A164517 Primes of the form 1+A162143(k).

4357, 12101, 16901, 28901, 52901, 164837, 184901, 220901, 224677, 417317, 427717, 682277, 792101, 820837, 894917, 972197, 1020101, 1110917, 1136357, 1144901, 1223237, 1313317, 1552517, 1887877, 1943237, 1976837, 2056357, 2464901

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 14 2009

Keywords

• nonn

Comments

Primes p such that p-1 equals the square of a product of three distinct primes.

Primes of the similar form A162143(k)-1 do not exist, because A162143 are squares

which allows for the obvious factorization A162143(k)-1 = (A007304(k)+1)*(A007304(k)-1).

Examples

			For p=4357=a(1), p=14356=2^2*3^2*11^2. For p=12101, p=1=12100=2^2*5^2*11^2.
		

Programs

Mathematica

f[n_]:=FactorInteger[n][[1,2]]==2&&Length[FactorInteger[n]]==3&&FactorInteger[n][[2, 2]]==2&&FactorInteger[n][[3,2]]==2; lst={};Do[p=Prime[n];If[f[p-1], AppendTo[lst,p]],{n,2,9!}];lst

Extensions

Edited by R. J. Mathar, Aug 18 2009