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Product of largest semiprime <= n and smallest semiprime >= n.
1

%I #8 Oct 03 2015 23:49:05

%S 16,24,36,54,54,81,100,140,140,140,196,225,315,315,315,315,315,441,

%T 484,550,550,625,676,858,858,858,858,858,858,1089,1156,1225,1330,1330,

%U 1444,1521,1794,1794,1794,1794,1794,1794,2116,2254,2254,2401,2499,2601,2805

%N Product of largest semiprime <= n and smallest semiprime >= n.

%C This is to A030664 as semiprimes A001358 are to primes A000040. Subset of A014613.

%F a(n) = MAX{j in A001358 and j <= n} * MIN{j in A001358 and j >= n}

%e a(10) = 100 because the largest semiprime <= 10 is 10, the smallest semiprime >= 10 is 10 and 10*10=100.

%p 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 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 Cf. A001358, A014613, A030664.

%K easy,nonn

%O 4,1

%A _Jonathan Vos Post_, May 09 2008

%E More terms from _R. J. Mathar_, May 11 2008