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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.
5
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
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;
MATHEMATICA
2^(2 * (p = MersennePrimeExponent[Range[9]]) + 1) * (2^p - 1)^2 (* Amiram Eldar, Jan 03 2020 *)
KEYWORD
nonn
AUTHOR
Walter Kehowski, Jan 01 2020
STATUS
approved