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%I #15 Mar 15 2023 12:48:34
%S 4,6,10,14,15,22,38,57,58,62,69,82,85,123,129,142,158,178,194,202,203,
%T 205,214,218,221,254,274,295,303,327,339,346,365,411,413,422,437,478,
%U 482,485,519,543,545,551,622,626,635,694,723,734,745,753,794,813,893
%N Semiprimes of the form m*p such that k*p=(m*p)-th semiprime.
%H David A. Corneth, <a href="/A175706/b175706.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=4 because 5*2=(2*2)-th semiprime, a(2)=6 because 5*3=(2*3)-th semiprime, a(3)=10 because 13*2=(5*2)-th semiprime, a(4)=14 because 19*2=(7*2)-th semiprime, a(5)=15 because 13*3=(5*3)-th semiprime, a(6)=22 because 31*2=(11*2)-th semiprime.
%p Contribution from _R. J. Mathar_, Aug 10 2010: (Start)
%p A001358 := proc(n) option remember; local a; if n = 1 then 4; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 2 then return a; end if; end do: end if; end proc:
%p for i from 1 to 300 do mp := A001358(i) ; kp := A001358(mp) ; p := igcd(mp,kp) ; if isprime(p) then printf("%d,",mp) ; end if; end do: (End)
%t SemiPrimeQ[n_Integer] := If[Abs[n]<2, False, (2==Plus@@Transpose[FactorInteger[Abs[n]]][[2]])]; sp=Select[Range[10000], SemiPrimeQ]; sp2=Select[sp, #<Length[sp]&]; Select[sp2, GCD[ #,sp[[ # ]]]>1&] (* _T. D. Noe_, Aug 11 2010 *)
%o (PARI) first(n) = {my(t = 0, res = List()); for(i = 1, oo, if(bigomega(i) == 2, t++; if(bigomega(t) == 2 && gcd(t, i) > 1, listput(res, t); if(#res >= n, return(res) ) ) ); ); res } \\ _David A. Corneth_, Mar 15 2023
%Y Cf. A000040, A001358.
%K nonn,less
%O 1,1
%A _Juri-Stepan Gerasimov_, Aug 10 2010
%E Corrected and extended by _R. J. Mathar_ and _T. D. Noe_, Aug 11 2010
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