cp's OEIS Frontend

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.

%I A330817 #19 Jan 07 2020 22:52:06
%S A330817 288,6272,1968128,528515072,9005000365703168,590286803193810649088,
%T A330817 151115150991626099228672,42535295825503226685013029169053827072,
%U A330817 56539106072908298497625662716064949049646203797489239767322203013731319808
%N 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.
%C A330817 Also numbers with power-spectral basis {M_p^2*(M_p+2)^2,(M_p^2-1)^2}.
%C A330817 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.
%H A330817 Walter Kehowski, <a href="/A330817/b330817.txt">Table of n, a(n) for n = 1..12</a>
%e A330817 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.
%p A330817 A330817:=[]:
%p A330817 for www to 1 do
%p A330817 for i from 1 to 31 do
%p A330817   #ithprime(31)=127
%p A330817   p:=ithprime(i);
%p A330817   q:=2^p-1;
%p A330817   if isprime(q) then x:=2^(2*p+1)*q^2; A330817:=[op(A330817),x]; fi;
%p A330817 od;
%p A330817 od;
%p A330817 A330817;
%t A330817 2^(2 * (p = MersennePrimeExponent[Range[9]]) + 1) * (2^p - 1)^2 (* _Amiram Eldar_, Jan 03 2020 *)
%Y A330817 Cf. A000043, A000668, A132794, A133049, A330818, A330819, A330820.
%K A330817 nonn
%O A330817 1,1
%A A330817 _Walter Kehowski_, Jan 01 2020