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

1,2

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A196527, A070826.

Sequence in context: A269347 A183554 A229847 * A110668 A367773 A176248

Adjacent sequences: A196526 A196527 A196528 * A196530 A196531 A196532

Keyword

nonn

Author

Reinhard Zumkeller, Oct 03 2011

Status

approved