This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A139096 #16 Oct 17 2024 08:24:12 %S A139096 4,24,480,8064,33546240,8589803520,137438429184,2305843007066210304, %T A139096 2658455991569831743501771111346995200, %U A139096 191561942608236107294793377774818628309652252823388160 %N A139096 Infraperfect numbers: a(n) = 2^(2*p - 1) - 2^p, where p is A000043(n). %C A139096 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. %H A139096 Amiram Eldar, <a href="/A139096/b139096.txt">Table of n, a(n) for n = 1..15</a> %H A139096 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>. %F A139096 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). %e A139096 a(2) = 24 because A000043(2) = 3 then 2^(2*3 - 1) - 2^3 = 2^5 - 2^3 = 32 - 8 = 24. %t A139096 Map[2^(2*#-1) - 2^# &, MersennePrimeExponent[Range[10]]] (* _Amiram Eldar_, Oct 17 2024 *) %Y A139096 Cf. A000043, A000396, A000668, A019279, A061652, A072868, A139306. %K A139096 nonn %O A139096 1,1 %A A139096 _Omar E. Pol_, Apr 22 2008 %E A139096 More terms from _R. J. Mathar_, Feb 05 2010