A249780 Product of lowest and highest prime factors of 2^n-1.

9, 49, 15, 961, 21, 16129, 51, 511, 93, 2047, 39, 67092481, 381, 1057, 771, 17179607041, 219, 274876858369, 123, 2359, 2049, 8388607, 723, 55831, 24573, 1838599, 381, 486737, 993, 4611686014132420609, 196611, 4196353, 393213, 3810551, 327, 137438953471, 1572861, 849583, 185043

Offset: 2

Author

Jacob Vecht, Nov 05 2014

Keywords

• nonn

Examples

			The lowest and higest prime factors of 2^6-1 are 3 and 7, so A(6) = 21
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..200

Programs

Maple

a:= proc(n) local F; F:= numtheory:-factorset(2^n-1); min(F)*max(F) end proc:
seq(a(n),n=2..50); # Robert Israel, Nov 05 2014

Mathematica

plhpf[n_]:=Module[{fn=FactorInteger[n]},fn[[1,1]]fn[[-1,1]]]; Table[plhpf [2^n-1],{n,2,40}] (* Harvey P. Dale, May 23 2020 *)

PARI

for(n=2, 50, p=2^n-1; print1(factor(p)[1, 1]*factor(p)[#factor(p)[, 1], 1], ", ")) \\ Derek Orr, Nov 05 2014

Python

from sympy import primefactors
A249780_list, x = [], 1
for n in range(2,10):
    x = 2*x + 1
    p = primefactors(x)
    A249780_list.append(max(p)*min(p)) # Chai Wah Wu, Nov 05 2014

Formula

a(n) = A005420(n) * A049479(n)

Extensions

More terms from Derek Orr, Nov 05 2014