login
A330840
a(n) = 4*M(n)^2*(M(n)+1)^2, where M(n) is the n-th Mersenne prime, A000668.
2
576, 12544, 3936256, 1057030144, 18010000731406336, 1180573606387621298176, 302230301983252198457344, 85070591651006453370026058338107654144, 113078212145816596995251325432129898099292407594978479534644406027462639616
OFFSET
1,1
COMMENTS
Also a(n+1) is the second element of the power-spectral basis of A330839(n), where by power-spectral we mean that the spectral basis consists of primes and powers.
LINKS
Garret Sobczyk, The Missing Spectral Basis in Algebra and Number Theory, The American Mathematical Monthly, Vol. 108, No. 4 (April 2001), pp. 336-346.
FORMULA
a(n) = 4 * A133049(n) * A330824(n).
EXAMPLE
a(2) = 4*7^2*2^(2*3) = 2^8*7^2 = 112^2, and the spectral basis of A330839(1) = 18816 is {63^2, 112^2, 48^2}, consisting only of powers.
MAPLE
A330840 := proc(n::posint)
local p, m;
p:=NumberTheory[IthMersenne](n);
m:=2^p-1;
return 4*m^2*(m+1)^2;
end:
MATHEMATICA
f[p_] := 2^(2*p + 2)*(2^p - 1)^2; f /@ MersennePrimeExponent /@ Range[9] (* Amiram Eldar, Jan 24 2020 *)
KEYWORD
nonn
AUTHOR
Walter Kehowski, Jan 23 2020
STATUS
approved