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a(n) = n + n-th semiprime.
7

%I #23 Apr 05 2023 09:14:44

%S 5,8,12,14,19,21,28,30,34,36,44,46,48,52,54,62,66,69,74,77,79,84,88,

%T 93,99,103,109,113,115,117,122,125,127,129,141,147,152,156,158,161,

%U 163,165,172,177,179,187,189,191,194,196,206,210,212,215,221,225,234,236

%N a(n) = n + n-th semiprime.

%C This is the semiprime analog of A014688.

%H Robert Israel, <a href="/A100493/b100493.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein, World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>.

%F a(n) = n + A001358(n).

%F a(n) ~ n log n / log log n. [_Charles R Greathouse IV_, Dec 28 2011]

%e a(7) = 7 + semiprime(7) = 7 + 21 = 28.

%p N:= 1000: # to use semiprimes <= N

%p Primes:= select(isprime, [2,seq(i,i=3..N,2)]):

%p Semiprimes:= sort(convert(select(`<=`,{seq(seq(Primes[i]*Primes[j],i=1..j),j=1..nops(Primes))},N),list)):

%p seq(i+Semiprimes[i],i=1..nops(Semiprimes)); # _Robert Israel_, Dec 20 2015

%t m=300;

%t A001358:= A001358= Select[Range[5*m], PrimeOmega[#]==2 &];

%t A100493[n_]:= n + A001358[[n]];

%t Table[A100493[n], {n, m}] (* _G. C. Greubel_, Apr 04 2023 *)

%o (Magma)

%o m:=300;

%o A001222:=[n eq 1 select 0 else (&+[p[2]: p in Factorization(n)]): n in [1..4*m]];

%o A001358:=[n: n in [1..4*m] | A001222[n] eq 2];

%o A100493:= func< n | n + A001358[n] >;

%o [A100493(n): n in [1..m]]; // _G. C. Greubel_, Apr 04 2023

%o (SageMath)

%o from sympy import primeomega

%o b=[n for n in (1..1000) if primeomega(n)==2]

%o [n+b[n-1] for n in range(1,301)] # _G. C. Greubel_, Apr 04 2023

%Y Cf. A001358, A014688, A100466, A100467, A100915, A100916.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Nov 20 2004

%E Edited, corrected and extended by _Ray Chandler_, Nov 26 2004