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A046315 Odd semiprimes: odd numbers divisible by exactly 2 primes (counted with multiplicity). 59
9, 15, 21, 25, 33, 35, 39, 49, 51, 55, 57, 65, 69, 77, 85, 87, 91, 93, 95, 111, 115, 119, 121, 123, 129, 133, 141, 143, 145, 155, 159, 161, 169, 177, 183, 185, 187, 201, 203, 205, 209, 213, 215, 217, 219, 221, 235, 237, 247, 249, 253, 259, 265, 267, 287, 289 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The number of odd semiprimes < 10^n: 1, 19, 204, 1956, 18245, 168497, 1555811, 14426124, 134432669, ...; see A085770. - Robert G. Wilson v, Aug 25 2011

In general, the prime factors, p, of a(n) are given by: p = sqrt(a(n) + (k/2)^2) +- (k/2) where k is the positive difference of the prime factors.  Equivalently, p = (1/2)( sqrt(4a(n) + k^2) +- k ). - Wesley Ivan Hurt, Jun 28 2013

LINKS

Zak Seidov and K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 1956 terms from Zak Seidov)

EXAMPLE

15 is in the sequence because it is odd number and also 15 = 3 * 5, which is semiprime. - K. D. Bajpai, Jul 05 2014

39 is in the sequence because it is odd number and also 39 = 3 * 13, which is semiprime. - K. D. Bajpai, Jul 05 2014

MAPLE

A046315 := proc(n) option remember; local r;

if n = 0 then RETURN(0) fi;

for r from A046315(n - 1) + 1 do

   if r mod 2 = 1 and numtheory[bigomega](r) = 2

   then RETURN(r) fi

od end:

seq(A046315(n), n=1..56); # Peter Luschny, Feb 15 2011

MATHEMATICA

Reap[Do[If[Total[FactorInteger[n]][[2]] == 2, Sow[n]], {n, 1, 400, 2}]][[2, 1]] (* Zak Seidov *)

fQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; Select[2 Range@ 150 - 1, fQ] (* Robert G. Wilson v, Feb 15 2011 *)

Select[Range[5, 301, 2], PrimeOmega[#]==2&] (* Harvey P. Dale, May 22 2015 *)

PROG

(PARI) list(lim)=my(u=primes(primepi(lim\3)), v=List(), t); for(i=2, #u, for(j=i, #u, t=u[i]*u[j]; if(t>lim, break); listput(v, t))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 19 2011

(Haskell)

a046315 n = a046315_list !! (n-1)

a046315_list = filter odd a001358_list  -- Reinhard Zumkeller, Jan 02 2014

CROSSREFS

Odd members of A001358.

A046388 is a subsequence.

Sequence in context: A225438 A175076 A046337 * A046372 A025045 A107987

Adjacent sequences:  A046312 A046313 A046314 * A046316 A046317 A046318

KEYWORD

nonn

AUTHOR

Patrick De Geest, Jun 15 1998

STATUS

approved

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Last modified January 18 20:19 EST 2018. Contains 297865 sequences.