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 A046882 #26 Feb 16 2025 08:32:39
%S A046882 1,1,4,46656,1333735776850284124449081472843776
%N A046882 Ultrafactorials: a(n) = n!^n!.
%C A046882 a(5) = 3175 042373 780336 892901 667920 556557 182493 442088 021222 004926 225128 381629 943118 937129 098831 435345 716937 405655 305190 657814 877412 786176 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000. - _Jonathan Vos Post_, Dec 09 2004
%C A046882 Note that, by analogy with factorial primes, subfactorial primes, superfactorial primes and hyperfactorial primes, if a(n)+1 or a(n)-1 is prime, it should be called an ultrafactorial prime. These begin: a(0)+1 = a(1)+1 = 2, a(2)-1 = 3, a(2)+1 = 5. Are there any more? Note that a(3) = 46657 = 13 * 37 * 97 is a 3-brilliant number. a(3)-5, a(3)-3 and a(3)+5 are semiprime; a(3)-7 and a(3)+7 are primes. - _Jonathan Vos Post_, Dec 09 2004
%H A046882 Jean-Christophe Pain, <a href="https://arxiv.org/abs/2408.00353">Bounds on the p-adic valuation of the factorial, hyperfactorial and superfactorial</a>, arXiv:2408.00353 [math.NT], 2024. See p. 6.
%H A046882 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ultrafactorial.html">Ultrafactorial</a>.
%F A046882 Sum_{n>=1} 1/a(n) = A100085. - _Amiram Eldar_, Nov 11 2020
%t A046882 lst={};Do[a=n!^n!;AppendTo[lst, a], {n, 6}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 01 2008 *)
%t A046882 #^#&/@(Range[0,5]!) (* _Harvey P. Dale_, Oct 15 2023 *)
%Y A046882 Cf. A002109, A100085.
%Y A046882 Cf. A000166, A000178, A002982.
%K A046882 nonn
%O A046882 0,3
%A A046882 Camillo Lamonaca (Camillo.Lamonaca(AT)dva.gov.au)