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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A013060 A012988 A261535 * A327020 A058233 A062635

Adjacent sequences: A188714 A188715 A188716 * A188718 A188719 A188720

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2011

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

Status

approved