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

1,2

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A002808, A071224.

Sequence in context: A210664 A176093 A092437 * A051012 A064644 A306444

Adjacent sequences: A064811 A064812 A064813 * A064815 A064816 A064817

Keyword

nice,nonn

Author

Reinhard Zumkeller, Oct 22 2001

Status

approved