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A113741 Pierpont 9-almost primes. 9-almost primes of form (2^K)*(3^L)+1.

%I A113741 #8 Feb 16 2025 08:32:59
%S A113741 1601009443167990625,1897492673384285185,39346408075296537575425,
%T A113741 46005119909369701466113,221073919720733357899777,
%U A113741 2153693963075557766310748,3925770232266214525108225
%N A113741 Pierpont 9-almost primes. 9-almost primes of form (2^K)*(3^L)+1.
%H A113741 Charles R Greathouse IV, <a href="/A113741/b113741.txt">Table of n, a(n) for n = 1..434</a>
%H A113741 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PierpontPrime.html">Pierpont Prime</a>
%H A113741 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>
%F A113741 a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 9.
%e A113741 a(1) = 1601009443167990625 = (2^5)*(3^35)+1 = 5 * 5 * 5 * 5 * 5 * 7 * 11 * 241 * 27608073601.
%e A113741 a(2) = 1897492673384285185 = (2^10)*(3^32)+1 = 5 * 13 * 13 * 13 * 41 * 41 * 373 * 2357 * 116881.
%o A113741 (PARI) list(lim)=my(v=List(), L=lim\1-1); for(e=0, logint(L, 3), my(t=3^e); while(t<=L, if(bigomega(t+1)==9, listput(v, t+1)); t*=2)); Set(v) \\ _Charles R Greathouse IV_, Feb 02 2017
%Y A113741 Intersection of A046312 and A055600.
%Y A113741 A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.
%Y A113741 A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.
%Y A113741 A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.
%Y A113741 A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1.
%Y A113741 A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.
%Y A113741 A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.
%Y A113741 A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.
%Y A113741 A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1.
%K A113741 easy,nonn
%O A113741 1,1
%A A113741 _Jonathan Vos Post_, Nov 08 2005
%E A113741 Extended by _Ray Chandler_, Nov 08 2005