A330817 Numbers of the form 2^(2*p+1)*M_p^2, where M_p is a Mersenne prime, A000668, with Mersenne exponent p, A000043.

288, 6272, 1968128, 528515072, 9005000365703168, 590286803193810649088, 151115150991626099228672, 42535295825503226685013029169053827072, 56539106072908298497625662716064949049646203797489239767322203013731319808

Offset

1,1

Comments

Also numbers with power-spectral basis {M_p^2*(M_p+2)^2,(M_p^2-1)^2}.

The first factor of a(n) is A330818. The first element of the spectral basis of a(n) is A330819, and the second element is A330820.

Links

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

Example

Since p=2 and M_2=3, then a(1)=2^(2*2+1)*3^3=288, and 288 has spectral basis {15^2, 2^6}, consisting of powers.

Maple

A330817:=[]:
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; A330817:=[op(A330817), x]; fi;
od;
od;
A330817;

Mathematica

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

Crossrefs

Cf. A000043, A000668, A132794, A133049, A330818, A330819, A330820.

Sequence in context: A332429 A232340 A290028 * A299860 A264204 A202165

Adjacent sequences: A330814 A330815 A330816 * A330818 A330819 A330820

Keyword

nonn

Author

Walter Kehowski, Jan 01 2020

Status

approved