A089195 Primes p such that all prime factors of p-1 have exponent 2.

5, 37, 101, 197, 677, 4357, 5477, 8837, 12101, 16901, 17957, 21317, 28901, 42437, 44101, 52901, 98597, 106277, 148997, 164837, 184901, 217157, 220901, 224677, 324901, 401957, 417317, 427717, 454277, 476101, 509797, 682277, 792101, 820837

Offset

1,1

Comments

This property for prime p-1 = cube only numbers does not hold since the sum of 2 cubes has factors and p-1 = q^3 => p = q^3+1 = sum of 2 cubes.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Example

101 is included because 100 = 2^2*5^2 only square factors. 109 is not because while 108=2^2*3^3 has a square only factor it also has a cube factor.

Mathematica

Select[Table[Prime[n], {n, 70000}], Length[Union[Last/@FactorInteger[#-1]]]==1&&Union[Last/@FactorInteger[#-1]]=={2}&] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2011 *)

Prog

(PARI) /* Input number of iterations n, power p and number to subtract k. */ powerfreep3(n, p, k) = { c=0; pc=0; forprime(x=2, n, pc++; if(!ispowerfree3(x-k, p), c++; print1(x", "); ) ); print(); print(c", "pc", "c/pc+.0) } ispowerfree3(m, p1) = { flag=1; y=component(factor(m), 2); for(i=1, length(y), if(y[i] == p1, flag=0, flag=1; break); ); return(flag) } /* this should be cleaned up, Joerg Arndt, Apr 09 2011 */

Crossrefs

Sequence in context: A054587 A099937 A142036 * A249861 A358035 A319485

Adjacent sequences: A089192 A089193 A089194 * A089196 A089197 A089198

Keyword

easy,nonn

Author

Cino Hilliard, Dec 08 2003

Status

approved