login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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 *)
CROSSREFS
Sequence in context: A236078 A264524 A209781 * A226285 A370226 A354021
KEYWORD
nonn
AUTHOR
Walter Kehowski, Jan 23 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 13 06:34 EDT 2024. Contains 374267 sequences. (Running on oeis4.)