A330818 Numbers of the form 2^(2*p+1), where p is a Mersenne exponent, A000043.

32, 128, 2048, 32768, 134217728, 34359738368, 549755813888, 9223372036854775808, 10633823966279326983230456482242756608, 766247770432944429179173513575154591809369561091801088

Offset: 1

Author

Walter Kehowski, Jan 01 2020

Keywords

• nonn

Comments

Also the first factor of A330817, 2^(2*p+1)*M_p^2. The second factor of A330817 is A133049.

Examples

			a(1) = 2^(2*2+1) = 32. Since M_2=3, the number 2^5*3^2 has power-spectral basis {225,64}.
		

Links

• Walter Kehowski, Table of n, a(n) for n = 1..12

Crossrefs

Cf. A000043, A000668, A132794, A133049, A330817, A330819, A330820.

Programs

Maple

A330818:=[]:
for www to 1 do
for i from 1 to 31 do
  #ithprime(31)=127
  p:=ithprime(i);
  q:=2^p-1;
  if isprime(q) then x:=2^(2*p+1); A330818:=[op(A330818),x]; fi;
od;
od;
A330818;

Mathematica

2^(2 * MersennePrimeExponent[Range[10]] + 1) (* Amiram Eldar, Jan 03 2020 *)

Formula

a(n) = 2^(2*A000043(n)+1).