

A046315


Odd semiprimes: odd numbers divisible by exactly 2 primes (counted with multiplicity).


116



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
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OFFSET

1,1


COMMENTS

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



FORMULA

Sum_{n>=1} 1/a(n)^s = (1/2)*(P(s)^2 + P(2*s))  P(s)/2^s, for s>1, where P is the prime zeta function.  Amiram Eldar, Nov 21 2020


EXAMPLE

15 is a term because it is an odd number and 15 = 3 * 5, which is semiprime.
39 is a term because it is an odd number and 39 = 3 * 13, which is semiprime. (End)


MAPLE

A046315 := proc(n) option remember; local r;
if n = 1 then RETURN(9) fi;
for r from procname(n  1) + 2 by 2 do
if numtheory[bigomega](r) = 2 then
RETURN(r)
end if
end do
end proc:


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 !! (n1)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



