A089200 Primes p such that p-1 is divisible by a cube.

17, 41, 73, 89, 97, 109, 113, 137, 163, 193, 233, 241, 251, 257, 271, 281, 313, 337, 353, 379, 401, 409, 433, 449, 457, 487, 521, 541, 569, 577, 593, 601, 617, 641, 673, 751, 757, 761, 769, 809, 811, 857, 881, 919, 929, 937, 953, 977

Offset: 1

Author

Cino Hilliard, Dec 08 2003

Keywords

• easy
• nonn

Comments

This sequence is infinite and its relative density in the sequence of primes is 1 - Product_{p prime} (1-1/(p^2*(p-1))) = 1 - A065414 = 0.30249864150363409671... (Jakimczuk, 2024). - Amiram Eldar, Jul 20 2024

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
• Rafael Jakimczuk, Numbers of the form p-1 where p is prime, ResearchGate preprint, 2024.

Crossrefs

Cf. A039787, A046099, A065414.

Programs

Mathematica

f[n_]:=Max[Last/@FactorInteger[n]]; lst={};Do[p=Prime[n];If[f[p-1]>=3,AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 03 2009 *)
Select[Prime[Range[200]],Count[Transpose[FactorInteger[#-1]][[2]], ?(#>2&)]>0&] (* _Harvey P. Dale, Jan 01 2012 *)

PARI

ispowerfree(m,p1) = { flag=1; y=component(factor(m),2); for(i=1,length(y), if(y[i] >= p1,flag=0;break); ); return(flag) }
powerfreep3(n,p,k) = { c=0; pc=0; forprime(x=2,n, pc++; if(ispowerfree(x+k,p)==0, c++; print1(x","); ) ); print(); print(c","pc","c/pc+.0) }