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A140135 Product of largest semiprime <= n and smallest semiprime >= n.

%I A140135 #8 Oct 03 2015 23:49:05
%S A140135 16,24,36,54,54,81,100,140,140,140,196,225,315,315,315,315,315,441,
%T A140135 484,550,550,625,676,858,858,858,858,858,858,1089,1156,1225,1330,1330,
%U A140135 1444,1521,1794,1794,1794,1794,1794,1794,2116,2254,2254,2401,2499,2601,2805
%N A140135 Product of largest semiprime <= n and smallest semiprime >= n.
%C A140135 This is to A030664 as semiprimes A001358 are to primes A000040. Subset of A014613.
%F A140135 a(n) = MAX{j in A001358 and j <= n} * MIN{j in A001358 and j >= n}
%e A140135 a(10) = 100 because the largest semiprime <= 10 is 10, the smallest semiprime >= 10 is 10 and 10*10=100.
%p A140135 isA001358 := proc(n) RETURN( numtheory[bigomega](n) = 2) ; end: A001358 := proc(n) option remember ; local a; if n = 1 then 4; else for a from A001358(n-1)+1 do if isA001358(a) then RETURN(a) ; fi ; od: fi ; end: prevsemiprime := proc(n) local a; for a from n to 4 by -1 do if isA001358(a) then RETURN(a) ; fi ; od: RETURN(-1) ; end: nextsemiprime := proc(n) local a; for a from n do if isA001358(a) then RETURN(a) ; fi ; od: RETURN(-1) ; end: A140135 := proc(n) prevsemiprime(n)*nextsemiprime(n) ; end: seq(A140135(n),n=4..80) ; # _R. J. Mathar_, May 11 2008
%t A140135 ls[n_]:=Module[{i=0},While[PrimeOmega[n+i]!=2,i++];n+i]; ss[n_]:=Module[ {i=0}, While[PrimeOmega[n-i]!=2,i++];n-i]; Table[ls[n]*ss[n],{n,4,60}] (* _Harvey P. Dale_, Oct 18 2013 *)
%Y A140135 Cf. A001358, A014613, A030664.
%K A140135 easy,nonn
%O A140135 4,1
%A A140135 _Jonathan Vos Post_, May 09 2008
%E A140135 More terms from _R. J. Mathar_, May 11 2008