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A113741 Pierpont 9-almost primes. 9-almost primes of form (2^K)*(3^L)+1. 7
1601009443167990625, 1897492673384285185, 39346408075296537575425, 46005119909369701466113, 221073919720733357899777, 2153693963075557766310748, 3925770232266214525108225 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 28 17:54 EST 2021. Contains 349415 sequences. (Running on oeis4.)