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A100493 a(n) = n + n-th semiprime.

%I A100493 #28 Mar 10 2025 11:51:29
%S A100493 5,8,12,14,19,21,28,30,34,36,44,46,48,52,54,62,66,69,74,77,79,84,88,
%T A100493 93,99,103,109,113,115,117,122,125,127,129,141,147,152,156,158,161,
%U A100493 163,165,172,177,179,187,189,191,194,196,206,210,212,215,221,225,234,236
%N A100493 a(n) = n + n-th semiprime.
%C A100493 This is the semiprime analog of A014688.
%H A100493 Robert Israel, <a href="/A100493/b100493.txt">Table of n, a(n) for n = 1..10000</a>
%H A100493 Eric Weisstein, World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>.
%F A100493 a(n) = n + A001358(n).
%F A100493 a(n) ~ n log n / log log n. [_Charles R Greathouse IV_, Dec 28 2011]
%e A100493 a(7) = 7 + semiprime(7) = 7 + 21 = 28.
%p A100493 N:= 1000: # to use semiprimes <= N
%p A100493 Primes:= select(isprime, [2,seq(i,i=3..N,2)]):
%p A100493 Semiprimes:= sort(convert(select(`<=`,{seq(seq(Primes[i]*Primes[j],i=1..j),j=1..nops(Primes))},N),list)):
%p A100493 seq(i+Semiprimes[i],i=1..nops(Semiprimes)); # _Robert Israel_, Dec 20 2015
%t A100493 m=300;
%t A100493 A001358:= A001358= Select[Range[5*m], PrimeOmega[#]==2 &];
%t A100493 A100493[n_]:= n + A001358[[n]];
%t A100493 Table[A100493[n], {n, m}] (* _G. C. Greubel_, Apr 04 2023 *)
%o A100493 (Magma)
%o A100493 m:=300;
%o A100493 A001222:=[n eq 1 select 0 else (&+[p[2]: p in Factorization(n)]): n in [1..4*m]];
%o A100493 A001358:=[n: n in [1..4*m] | A001222[n] eq 2];
%o A100493 A100493:= func< n | n + A001358[n] >;
%o A100493 [A100493(n): n in [1..m]]; // _G. C. Greubel_, Apr 04 2023
%o A100493 (SageMath)
%o A100493 from sympy import primeomega
%o A100493 b=[n for n in (1..1000) if primeomega(n)==2]
%o A100493 [n+b[n-1] for n in range(1,301)] # _G. C. Greubel_, Apr 04 2023
%o A100493 (PARI) lista(n)= my(s=0); vector(n, i, while(2!=bigomega(s++), ); i+s); \\ _Ruud H.G. van Tol_, Mar 10 2025
%Y A100493 Cf. A001358, A014688, A100466, A100467, A100915, A100916.
%K A100493 easy,nonn
%O A100493 1,1
%A A100493 _Jonathan Vos Post_, Nov 20 2004
%E A100493 Edited, corrected and extended by _Ray Chandler_, Nov 26 2004