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A089195 Primes p such that all prime factors of p-1 have exponent 2. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A319485 A201119

Adjacent sequences:  A089192 A089193 A089194 * A089196 A089197 A089198

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Dec 08 2003

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)