A330819 Numbers of the form M_p^2(M^p+2)^2, where M_p is a Mersenne prime (A000668) and p is a Mersenne exponent (A000043). Also the first element of the spectral basis of A330817.

225, 3969, 1046529, 268402689, 4503599493152769, 295147905144993087489, 75557863725364567605249, 21267647932558653957237540927630737409, 28269553036454149273332760011886696242605918383730576346715242738439159809

Offset: 1

Author

Walter Kehowski, Jan 01 2020

Keywords

• nonn

Comments

The second element of the spectral basis of A330817 is A330820.

Examples

			If p=2, then M_2=3, and a(1) = 3^2(3+2)^2 = 15^2 = 225.
		

Links

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

Crossrefs

Cf. A000043, A000668, A132794, A133049, A330817, A330818, A330820.

Programs

Maple

A330819:=[]:
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)*q^2; A330819:=[op(A330819),x]; fi;
od;
od;
A330819;

Mathematica

(m = 2^MersennePrimeExponent[Range[9]] - 1)^2 * (m + 2)^2 (* Amiram Eldar, Jan 03 2020 *)

Formula

a(n) = A000668(n)^2*(A000668(n)+2)^2.