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 A111346 Pierpont 6-almost primes. 6-almost primes of form (2^K)*(3^L)+1. 6
 14348908, 134217729, 1073741825, 139314069505, 231928233985, 264479053825, 282429536482, 618475290625, 705277476865, 3570467226625, 4398046511105, 8349416423425, 21134460321793, 35664401793025, 91507169819845 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..15. Eric Weisstein's World of Mathematics, Pierpont Prime Eric Weisstein's World of Mathematics, Almost Prime FORMULA a(n) is in this sequence iff there exist nonnegative integers K and L such that Omega((2^K)*(3^L)+1) = 6. EXAMPLE a(1) = 14348908 = (2^0)*(3^15)+1 = 2 * 2 * 7 * 31 * 61 * 271. a(2) = 134217729 = (2^27)*(3^0)+1 = 3 * 3 * 3 * 3 * 19 * 87211. a(3) = 1073741825 = (2^30)*(3^0)+1 = 5 * 5 * 13 * 41 * 61 * 1321. a(4) = 139314069505 = (2^18)*(3^12)+1 = 5 * 13 * 17 * 61 * 337 * 6133. a(100) = 151115727451828646838273 = (2^77)*(3^0)+1 = 3 * 43 * 617 * 683 * 78233 * 35532364099. a(127) = 9671406556917033397649409 = (2^83)*(3^0)+1 = 3 * 499 * 1163 * 2657 * 155377 * 13455809771. a(153) = 523347633027360537213511522 = (2^0)*(3^56)+1 = 2 * 17 * 113 * 193 * 19489 * 36214795668330833. a(169) = 2475880078570760549798248449 = (2^91)*(3^0)+1 = 3 * 43 * 2731 * 224771 * 1210483 * 25829691707. PROG (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 CROSSREFS Intersection of A046306 and A055600. A005109 gives the Pierpont primes, which are primes of the form (2^K)*(3^L)+1. A113432 gives the Pierpont semiprimes, 2-almost primes of the form (2^K)*(3^L)+1. A112797 gives the Pierpont 3-almost primes, of the form (2^K)*(3^L)+1. A111344 gives the Pierpont 4-almost primes, of the form (2^K)*(3^L)+1. A111345 gives the Pierpont 5-almost primes, of the form (2^K)*(3^L)+1. A113739 gives the Pierpont 7-almost primes, of the form (2^K)*(3^L)+1. A113740 gives the Pierpont 8-almost primes, of the form (2^K)*(3^L)+1. A113741 gives the Pierpont 9-almost primes, of the form (2^K)*(3^L)+1. Sequence in context: A237141 A204952 A210019 * A238080 A251009 A136608 Adjacent sequences: A111343 A111344 A111345 * A111347 A111348 A111349 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Nov 08 2005 EXTENSIONS Extended by Ray Chandler, Nov 08 2005 STATUS approved

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Last modified April 22 19:08 EDT 2024. Contains 371906 sequences. (Running on oeis4.)