A330839 -id:A330839 - cp's OEIS frontend

A330840 a(n) = 4M(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

Walter Kehowski, Jan 23 2020

nonn

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.

			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.

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

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

A330840 := proc(n::posint)
  local p, m;
  p:=NumberTheory[IthMersenne](n);
  m:=2^p-1;
  return 4*m^2*(m+1)^2;
end:

f[p_] := 2^(2*p + 2)*(2^p - 1)^2; f /@ MersennePrimeExponent /@ Range[9] (* Amiram Eldar, Jan 24 2020 *)

a(n) = 4 * A133049(n) * A330824(n).

cp's OEIS Frontend

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

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cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

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