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A113741 Pierpont 9-almost primes. 9-almost primes of form (2^K)*(3^L)+1. 7

%I #7 Feb 02 2017 12:25:58

%S 1601009443167990625,1897492673384285185,39346408075296537575425,

%T 46005119909369701466113,221073919720733357899777,

%U 2153693963075557766310748,3925770232266214525108225

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

%H Charles R Greathouse IV, <a href="/A113741/b113741.txt">Table of n, a(n) for n = 1..434</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PierpontPrime.html">Pierpont Prime</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>

%F a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 9.

%e a(1) = 1601009443167990625 = (2^5)*(3^35)+1 = 5 * 5 * 5 * 5 * 5 * 7 * 11 * 241 * 27608073601.

%e a(2) = 1897492673384285185 = (2^10)*(3^32)+1 = 5 * 13 * 13 * 13 * 41 * 41 * 373 * 2357 * 116881.

%o (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 Intersection of A046312 and A055600.

%Y A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1.

%Y A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1.

%Y A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1.

%Y A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1.

%Y A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1.

%Y A111346 gives the Pierpont 6-almost primes, of the form (2^K)*(3^L)+1.

%Y A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1.

%Y A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Nov 08 2005

%E Extended by _Ray Chandler_, Nov 08 2005

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)