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

1601009443167990625, 1897492673384285185, 39346408075296537575425, 46005119909369701466113, 221073919720733357899777, 2153693963075557766310748, 3925770232266214525108225

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..434

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) = 9.

Example

a(1) = 1601009443167990625 = (2^5)*(3^35)+1 = 5 * 5 * 5 * 5 * 5 * 7 * 11 * 241 * 27608073601.
a(2) = 1897492673384285185 = (2^10)*(3^32)+1 = 5 * 13 * 13 * 13 * 41 * 41 * 373 * 2357 * 116881.

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)==9, listput(v, t+1)); t*=2)); Set(v) \\ Charles R Greathouse IV, Feb 02 2017

Crossrefs

Intersection of A046312 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.

A111346 gives the Pierpont 6-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.

Sequence in context: A281506 A281507 A160045 * A115529 A229864 A113740

Adjacent sequences: A113738 A113739 A113740 * A113742 A113743 A113744

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 08 2005

Extensions

Extended by Ray Chandler, Nov 08 2005

Status

approved