A089195 -id:A089195 - 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

A188717 Primes p such that all prime factors of p-1 have exponent 4.

Original entry on oeis.org

2, 17, 1297, 1336337, 4477457, 29986577, 45212177, 126247697, 193877777, 406586897, 562448657, 916636177, 1416468497, 1944810001, 3208542737, 4162314257, 5006411537, 5972816657, 12444741137, 19565295377, 34188010001, 38167092497, 47156728337, 59553569297, 61505984017

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 09 2011

nonn

			17-1 = 2^4, 1297-1 = 2^4*3^4, 1336337-1 = 2^4*17^4, 4477457-1 = 2^4*23^4, ...

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A089195 (exponent 2), A037896 (primes of the form k^4+1), A188764.

Prepend[Select[Table[Prime[n],{n,600000}],Length[Union[Last/@FactorInteger[#-1]]]==1&&Union[Last/@FactorInteger[#-1]]=={4}&], 2]
seq[lim_] := Select[Select[Range[Floor[Surd[lim-1, 2]]], SquareFreeQ]^4 + 1, PrimeQ]; seq[10^6] (* Amiram Eldar, Jan 18 2025 *)

list(lim) = select(isprime, apply(x -> x^4 + 1, select(issquarefree, vector(sqrtnint(lim-1, 4), i, i)))); \\ Amiram Eldar, Jan 18 2025

a(12)-a(22) from Donovan Johnson, Apr 10 2011

a(1) = 2 inserted and a(23)-a(25) added 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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