A188717 - OEIS

%I #22 Jan 18 2025 09:06:51

%S 2,17,1297,1336337,4477457,29986577,45212177,126247697,193877777,

%T 406586897,562448657,916636177,1416468497,1944810001,3208542737,

%U 4162314257,5006411537,5972816657,12444741137,19565295377,34188010001,38167092497,47156728337,59553569297,61505984017

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

%H Amiram Eldar, <a href="/A188717/b188717.txt">Table of n, a(n) for n = 1..10000</a>

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

%t Prepend[Select[Table[Prime[n],{n,600000}],Length[Union[Last/@FactorInteger[#-1]]]==1&&Union[Last/@FactorInteger[#-1]]=={4}&], 2]

%t seq[lim_] := Select[Select[Range[Floor[Surd[lim-1, 2]]], SquareFreeQ]^4 + 1, PrimeQ]; seq[10^6] (* _Amiram Eldar_, Jan 18 2025 *)

%o (PARI) list(lim) = select(isprime, apply(x -> x^4 + 1, select(issquarefree, vector(sqrtnint(lim-1, 4), i, i)))); \\ _Amiram Eldar_, Jan 18 2025

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

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 09 2011

%E a(12)-a(22) from _Donovan Johnson_, Apr 10 2011

%E a(1) = 2 inserted and a(23)-a(25) added by _Amiram Eldar_, Jan 18 2025