A196529 Half of greatest common divisor of products of first n prime numbers and first n composite numbers.

1, 3, 3, 3, 15, 15, 105, 105, 105, 105, 105, 105, 1155, 1155, 1155, 15015, 15015, 15015, 15015, 15015, 15015, 255255, 255255, 255255, 4849845, 4849845, 4849845, 4849845, 4849845, 4849845, 111546435, 111546435, 111546435, 111546435, 111546435, 111546435

Offset: 1

Author

Reinhard Zumkeller, Oct 03 2011

Keywords

• nonn

Comments

a(n) = gcd(A002110(n),A036691(n)) / 2.

Examples

			a(3) = gcd(2*3*5,4*6*8)/2 = gcd(30,192)/2 = 6/2 = 3;
a(4) = gcd(2*3*5*7,4*6*8*9)/2 = gcd(210,1728)/2 = 6/2 = 3;
a(5) = gcd(2*3*5*7*11,4*6*8*9*10)/2 = gcd(2310,17280)/2 = 30/2 = 15.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A196527, A070826.

Programs

Mathematica

nn=40;With[{prs=Prime[Range[nn]],comps=Take[Complement[Range[Prime[nn]], Prime[ Range[nn]]],nn]},Rest[Table[GCD[Times@@Take[prs,n], Times@@Take[ comps,n]]/2,{n,nn}]]] (* Harvey P. Dale, Oct 16 2011 *)