A139096 Infraperfect numbers: a(n) = 2^(2*p - 1) - 2^p, where p is A000043(n).

4, 24, 480, 8064, 33546240, 8589803520, 137438429184, 2305843007066210304, 2658455991569831743501771111346995200, 191561942608236107294793377774818628309652252823388160

Offset: 1

Author

Omar E. Pol, Apr 22 2008

Keywords

• nonn

Comments

Difference between n-th even perfect number and n-th even superperfect number A061652(n). Difference between n-th ultraperfect number A139306(n) and n-th Mersenne prime A000668(n), minus 1. Also, difference between n-th perfect number A000396(n) and n-th superperfect number A019279(n), if there are no odd perfect and superperfect numbers.

Examples

			a(2) = 24 because A000043(2) = 3 then 2^(2*3 - 1) - 2^3 = 2^5 - 2^3 = 32 - 8 = 24.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..15
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Crossrefs

Cf. A000043, A000396, A000668, A019279, A061652, A072868, A139306.

Programs

Mathematica

Map[2^(2*#-1) - 2^# &, MersennePrimeExponent[Range[10]]] (* Amiram Eldar, Oct 17 2024 *)

Formula

a(n) = 2^(2*A000043(n) - 1) - 2^A000043(n) = A139306(n) - 2^A000043(n) = A139306(n) - A000668(n) - 1 = A139306(n) - (A000668(n)+1) = A139306(n) - 2*A061652(n) = A139306(n) - A072868(n).

Extensions

More terms from R. J. Mathar, Feb 05 2010