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%I #17 Oct 21 2023 17:04:39
%S 209,510509,6469693229,200560490129,13082761331670029,
%T 1922760350154212639069,557940830126698960967415389,
%U 40729680599249024150621323469,2305567963945518424753102147331756069,232862364358497360900063316880507363069
%N Semiprimes of the form primorial(k) - 1.
%H Sebastian Martin Ruiz, <a href="https://www.jstor.org/stable/3619207">A Result on Prime Numbers</a>, Math. Gaz. 81, 269, 1997.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Primorial.html">Primorial.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime.</a>
%F n# - 1 iff semiprime. Equals {A002110(i) - 1} intersection {A001358(j)}.
%e 4# - 1 = 209 = 11 * 19.
%e 7# - 1 = 510509 = 61 * 8369.
%e 10# - 1 = 6469693229 = 79 * 81894851.
%t Bigomega[n_]:=Plus@@Last/@FactorInteger[n]; SemiprimeQ[n_]:=Bigomega[n]==2; Primorial[n_]:=Product[Prime[i], {i, n}]; Select[Table[Primorial[n]-1, {n, 30}], SemiprimeQ] (* _Ray Chandler_, Mar 28 2005 *)
%Y Cf. A001358, A002110, A034386, A005234, A014545, A018239, A006794, A057704, A057705, A104877.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Mar 28 2005
%E Entry revised by _N. J. A. Sloane_, Apr 01 2006
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