A188717 -id:A188717 - cp's OEIS frontend

A188764 Primes p such that all prime factors of p-2 have exponent 3.

3, 29, 127, 24391, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 5177719, 9129331, 9938377, 10503461, 12326393, 15438251, 18191449, 24642173, 26730901, 28372627, 30080233, 39651823

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 09 2011

nonn

A048636 is the subsequence of terms where there is only one prime divisor of p-2. - M. F. Hasler, Jan 13 2025

			30080233-2 = 311^3, 39651823-2 = 11^3*31^3, ...
3-2 = 1 has no prime factors, so is trivially a member.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Subsequence of A144953; A048636 is a subsequence.

Cf. A089195, A188717.

Prepend[Select[Table[Prime[n],{n,3000000}],Length[Union[Last/@FactorInteger[#-2]]]==1&&Union[Last/@FactorInteger[#-2]]=={3}&], 3]
Prepend[Select[Prime[Range[25*10^5]],Union[FactorInteger[#-2][[All,2]]]=={3}&], 3] (* Harvey P. Dale, Nov 22 2018 *)
seq[lim_] := Select[Select[Range[Floor[Surd[lim-2, 3]]], SquareFreeQ]^3 + 2, PrimeQ]; seq[4*10^7] (* Amiram Eldar, Jan 18 2025 *)

list(lim)=my(v=List()); forsquarefree(k=1,sqrtnint(lim\1-2,3), my(p=k[1]^3+2); if(isprime(p), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 14 2025

a(n) >> n^3. - Charles R Greathouse IV, Jan 14 2025

a(1) = 3 inserted by Charles R Greathouse IV, Jan 14 2025

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

Original entry on oeis.org

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

Cino Hilliard, Dec 08 2003

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.

			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.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 2..301 from Vincenzo Librandi)

Cf. A188764, A188717.

Prepend[Select[Table[Prime[n],{n,70000}],Length[Union[Last/@FactorInteger[#-1]]]==1&&Union[Last/@FactorInteger[#-1]]=={2}&], 2] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2011 *)
seq[lim_] := Select[Select[Range[Floor[Surd[lim-1, 2]]], SquareFreeQ]^2 + 1, PrimeQ]; seq[10^6] (* Amiram Eldar, Jan 18 2025 *)

list(lim) = select(isprime, apply(x -> x^2 + 1, select(issquarefree, vector(sqrtnint(lim-1, 2), i, i)))); \\ Amiram Eldar, Jan 18 2025

a(1) = 2 inserted by Amiram Eldar, Jan 18 2025

cp's OEIS Frontend

A188764 Primes p such that all prime factors of p-2 have exponent 3.

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