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a(n) = floor(semiprime(n)/n).
2

%I #10 Oct 11 2024 12:45:55

%S 4,3,3,2,2,2,3,2,2,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,2,2,2,2,2,2,

%T 3,3,3,3,3,3,2,2,3,3,2,3,3,2,2,2,3,3,3,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,

%U 3,3,3,3,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3

%N a(n) = floor(semiprime(n)/n).

%C The ratio is an integer for n = 1, 2, 3, 11, 43, 53, ...

%H Andrew Howroyd, <a href="/A120927/b120927.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = floor(A001358(n)/n).

%e a(1) = floor(4/1) = 4 because 4 is the first semiprime.

%e a(2) = floor(6/2) = 3 because 6 is the second semiprime.

%e a(3) = floor(9/3) = 3 because 9 is the third semiprime.

%e a(4) = floor(10/4) = 2 because 4 is the fourth semiprime.

%t sp=Select[Range[290],PrimeOmega[#]==2&];l=Length[sp];Table[Floor[sp[[n]]/n],{n,l}] (* _James C. McMahon_, Oct 11 2024 *)

%o (PARI) seq(n)={my(a=vector(n), k=1, i=0); while(k<=#a, i++; if(bigomega(i)==2, a[k]=i\k; k++)); a} \\ _Andrew Howroyd_, Nov 08 2019

%Y Cf. A001358.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 18 2006

%E Terms a(61) and beyond from _Andrew Howroyd_, Nov 08 2019