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A046315
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Odd semiprimes: odd numbers divisible by exactly 2 primes (counted with multiplicity).
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104
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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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internal format)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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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
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EXAMPLE
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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)
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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