A383065 - OEIS

A383065

Integers k such that (k/rad(k))*2^rad(k) - 1 is prime where rad = A007947.

2, 3, 4, 5, 7, 9, 12, 13, 16, 17, 18, 19, 27, 31, 36, 50, 60, 61, 64, 80, 89, 107, 108, 112, 127, 135, 147, 189, 200, 212, 243, 252, 343, 448, 464, 500, 521, 576, 600, 607, 612, 648, 675, 688, 756, 768, 784, 800, 832, 875, 900, 1058, 1212, 1279, 1280

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

12 is a term because (12/6)*2^6 - 1 = 127 is prime, where d = 6 is largest squarefree divisor d of k = 12.

MATHEMATICA

s={}; Do[r=Last[Select[Divisors[n], SquareFreeQ]]; If[PrimeQ[2^r*n/r-1], AppendTo[s, n]], {n, 1280}]; s (* James C. McMahon, May 01 2025 *)

PROG

(Magma) [k: k in [1..1300] | IsPrime((k div &*PrimeDivisors(k))*2^&*PrimeDivisors(k)-1)];

(PARI) isok(k) = my(r=factorback(factorint(k)[, 1])); ispseudoprime((k/r)*2^r - 1); \\ Michel Marcus, Apr 20 2025

CROSSREFS

Supersequence of A000043 and A172461.

Cf. A002234, A003557, A007947.

Sequence in context: A238486 A238482 A395824 * A368483 A033100 A030741

Adjacent sequences: A383062 A383063 A383064 * A383066 A383067 A383068

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Apr 19 2025

STATUS

approved