A064814 Greatest common divisor of n and the n-th composite number.

1, 2, 1, 1, 5, 6, 7, 1, 1, 2, 1, 3, 1, 2, 5, 2, 1, 2, 1, 4, 3, 2, 1, 12, 1, 13, 1, 14, 1, 15, 1, 16, 1, 2, 1, 4, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 4, 1, 10, 3, 2, 1, 2, 11, 2, 1, 1, 1, 12, 1, 2, 3, 8, 5, 1, 1, 1, 1, 5, 1, 2, 1, 2, 3, 4, 7, 2, 1, 10, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 31, 1, 1, 32, 1, 2

Offset: 1

Author

Reinhard Zumkeller, Oct 22 2001

Keywords

• nice
• nonn

Comments

a(12) = gcd(12, A002808(12)) = gcd(12, 21) = gcd(2*2*3, 3*7) = 3.

Links

• R. Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A071224.

Programs

Mathematica

Composite[n_Integer] := FixedPoint[n + PrimePi[#] + 1 &, n + PrimePi[n] + 1]; Table[GCD[n, Composite[n]], {n, 100}] (* T. D. Noe, Feb 22 2012 *)
Module[{nn=150,comps},comps=Complement[Range[2,nn],Prime[Range[ PrimePi[ nn]]]];GCD@@@Thread[{comps,Range[Length[comps]]}]] (* Harvey P. Dale, Apr 23 2014 *)

PARI

nextComp(n)= { if (!isprime(n), return(n)); return(n + 1) } { c=3; for (n=1, 1000, c=nextComp(c + 1); write("b064814.txt", n, " ", gcd(n, c)) ) } \\ Harry J. Smith, Sep 27 2009

Formula

a(n) = gcd(n, A002808(n)).