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

16, 24, 36, 54, 54, 81, 100, 140, 140, 140, 196, 225, 315, 315, 315, 315, 315, 441, 484, 550, 550, 625, 676, 858, 858, 858, 858, 858, 858, 1089, 1156, 1225, 1330, 1330, 1444, 1521, 1794, 1794, 1794, 1794, 1794, 1794, 2116, 2254, 2254, 2401, 2499, 2601, 2805

Offset: 4

Author

Jonathan Vos Post, May 09 2008

Keywords

• easy
• nonn

Comments

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

Examples

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

Crossrefs

Cf. A001358, A014613, A030664.

Programs

Maple

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

Mathematica

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 *)

Formula

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

Extensions

More terms from R. J. Mathar, May 11 2008