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

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

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2011

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

Extensions

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