cp's OEIS Frontend

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.

%I A330819 #18 Jan 07 2020 22:53:37
%S A330819 225,3969,1046529,268402689,4503599493152769,295147905144993087489,
%T A330819 75557863725364567605249,21267647932558653957237540927630737409,
%U A330819 28269553036454149273332760011886696242605918383730576346715242738439159809
%N 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.
%C A330819 The second element of the spectral basis of A330817 is A330820.
%H A330819 Walter Kehowski, <a href="/A330819/b330819.txt">Table of n, a(n) for n = 1..12</a>
%F A330819 a(n) = A000668(n)^2*(A000668(n)+2)^2.
%e A330819 If p=2, then M_2=3, and a(1) = 3^2(3+2)^2 = 15^2 = 225.
%p A330819 A330819:=[]:
%p A330819 for www to 1 do
%p A330819 for i from 1 to 31 do
%p A330819   #ithprime(31)=127
%p A330819   p:=ithprime(i);
%p A330819   q:=2^p-1;
%p A330819   if isprime(q) then x:=2^(2*p+1)*q^2; A330819:=[op(A330819),x]; fi;
%p A330819 od;
%p A330819 od;
%p A330819 A330819;
%t A330819 (m = 2^MersennePrimeExponent[Range[9]] - 1)^2 * (m + 2)^2 (* _Amiram Eldar_, Jan 03 2020 *)
%Y A330819 Cf. A000043, A000668, A132794, A133049, A330817, A330818, A330820.
%K A330819 nonn
%O A330819 1,1
%A A330819 _Walter Kehowski_, Jan 01 2020