A111346 - OEIS

%I #7 Feb 01 2017 15:31:42

%S 14348908,134217729,1073741825,139314069505,231928233985,264479053825,

%T 282429536482,618475290625,705277476865,3570467226625,4398046511105,

%U 8349416423425,21134460321793,35664401793025,91507169819845

%N Pierpont 6-almost primes. 6-almost primes of form (2^K)*(3^L)+1.

%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) = 6.

%e a(1) = 14348908 = (2^0)*(3^15)+1 = 2 * 2 * 7 * 31 * 61 * 271.

%e a(2) = 134217729 = (2^27)*(3^0)+1 = 3 * 3 * 3 * 3 * 19 * 87211.

%e a(3) = 1073741825 = (2^30)*(3^0)+1 = 5 * 5 * 13 * 41 * 61 * 1321.

%e a(4) = 139314069505 = (2^18)*(3^12)+1 = 5 * 13 * 17 * 61 * 337 * 6133.

%e a(100) = 151115727451828646838273 = (2^77)*(3^0)+1 = 3 * 43 * 617 * 683 * 78233 * 35532364099.

%e a(127) = 9671406556917033397649409 = (2^83)*(3^0)+1 = 3 * 499 * 1163 * 2657 * 155377 * 13455809771.

%e a(153) = 523347633027360537213511522 = (2^0)*(3^56)+1 = 2 * 17 * 113 * 193 * 19489 * 36214795668330833.

%e a(169) = 2475880078570760549798248449 = (2^91)*(3^0)+1 = 3 * 43 * 2731 * 224771 * 1210483 * 25829691707.

%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)==6, listput(v, t+1)); t*=2)); Set(v) \\ _Charles R Greathouse IV_, Feb 01 2017

%Y Intersection of A046306 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 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.

%Y A113741 gives the Pierpont 9-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