A330840 a(n) = 4*M(n)^2*(M(n)+1)^2, where M(n) is the n-th Mersenne prime, A000668.

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

Table of n, a(n) for n=1..9.

Garret Sobczyk, The Missing Spectral Basis in Algebra and Number Theory, The American Mathematical Monthly, Vol. 108, No. 4 (April 2001), pp. 336-346.

Wikipedia, Idempotent (ring theory)

Wikipedia, Peirce decomposition

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

Cf. A000043, A000668, A133049, A330818, A330819, A330820, A330839.

Sequence in context: A236078 A264524 A209781 * A226285 A370226 A354021

Adjacent sequences: A330837 A330838 A330839 * A330841 A330842 A330843

Keyword

nonn

Author

Walter Kehowski, Jan 23 2020

Status

approved