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A046882 Ultrafactorials: a(n) = n!^n!. 10
1, 1, 4, 46656, 1333735776850284124449081472843776 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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
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
LINKS
Eric Weisstein's World of Mathematics, Ultrafactorial.
FORMULA
Sum_{n>=1} 1/a(n) = A100085. - Amiram Eldar, Nov 11 2020
MATHEMATICA
lst={}; Do[a=n!^n!; AppendTo[lst, a], {n, 6}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 01 2008 *)
#^#&/@(Range[0, 5]!) (* Harvey P. Dale, Oct 15 2023 *)
CROSSREFS
Sequence in context: A173138 A275587 A132638 * A165812 A218405 A259492
KEYWORD
nonn
AUTHOR
Camillo Lamonaca (Camillo.Lamonaca(AT)dva.gov.au)
STATUS
approved

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Last modified March 19 07:49 EDT 2024. Contains 370958 sequences. (Running on oeis4.)