

A252656


Numbers n such that 3^n  n is a semiprime.


8



4, 6, 10, 25, 28, 32, 98, 124, 146, 164, 182, 190, 200, 220, 226, 230, 248, 280, 362, 376, 418, 446, 518, 544
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OFFSET

1,1


COMMENTS

Are there odd members of the sequence other than 25? There are no others < 10000. An odd number m is in the sequence iff (3^m  m)/2 is prime.  Robert Israel, Jan 02 2015
No more odd terms after a(4) = 25 for m < 200000. a(25) >= 626.  Hugo Pfoertner, Aug 07 2019


LINKS

Table of n, a(n) for n=1..24.
factordb.com, Status of 3^626626.


EXAMPLE

4 is in this sequence because 3^4  4 = 7*11 is semiprime.
10 is in this sequence because 3^10  10 = 43*1373 and these two factors are prime.


MAPLE

select(n > numtheory:bigomega(3^n  n) = 2, [$1..150]); # Robert Israel, Jan 02 2015


MATHEMATICA

Select[Range[150], PrimeOmega[3^#  #] == 2 &]


PROG

(MAGMA) IsSemiprime:=func<i  &+[d[2]: d in Factorization(i)] eq 2>; [m: m in [2..150]  IsSemiprime(s) where s is 3^mm];
(PARI) is(m) = bigomega(3^mm)==2 \\ Felix Fröhlich, Dec 30 2014
(PARI) n=1; while(n<100, s=3^nn; c=0; forprime(p=1, 10^4, if(s%p, c++); if(s%p==0, s1=s/p; if(ispseudoprime(s1), print1(n, ", "); c=0; break); if(!ispseudoprime(s1), c=0; break))); if(!c, n++); if(c, if(bigomega(s)==2, print1(n, ", ")); n++)) \\ Derek Orr, Jan 02 2015


CROSSREFS

Cf. numbers m such that k^m  m is a semiprime: A165767 (k = 2), this sequence (k = 3), A252657 (k = 4), A252658 (k = 5), A252659 (k = 6), A252660 (k = 7), A252661 (k = 8), A252662 (k = 9), A252663 (k = 10).
Cf. A001358 (semiprimes), A058037, A252788.
Sequence in context: A277343 A077065 A131867 * A322961 A291542 A242565
Adjacent sequences: A252653 A252654 A252655 * A252657 A252658 A252659


KEYWORD

nonn,more,hard


AUTHOR

Vincenzo Librandi, Dec 20 2014


EXTENSIONS

a(10) from Felix Fröhlich, Dec 30 2014
a(11)a(14) from Charles R Greathouse IV, Jan 02 2015
a(15)a(24) from Luke March, Aug 21 2015


STATUS

approved



