A111426 Difference between largest and smallest prime factor of the n-th composite number.

0, 1, 0, 0, 3, 1, 5, 2, 0, 1, 3, 4, 9, 1, 0, 11, 0, 5, 3, 0, 8, 15, 2, 1, 17, 10, 3, 5, 9, 2, 21, 1, 0, 3, 14, 11, 1, 6, 5, 16, 27, 3, 29, 4, 0, 8, 9, 15, 20, 5, 1, 35, 2, 17, 4, 11, 3, 0, 39, 5, 12, 41, 26, 9, 3, 6, 21, 28, 45, 14, 1, 5, 8, 3, 15, 11, 4, 51, 1, 9, 34, 5, 17, 18, 27, 10, 57, 10, 3, 0

Offset: 1

Author

Giovanni Teofilatto, Nov 13 2005

Keywords

• nonn

Comments

a(n) = 0 iff the n-th composite number is a perfect power.

First occurrence of k or 0 if impossible: 2,8,5,12,7,38,0,21,13,26,16,61,0,35,22,40,25,84,0,49,31,156,0,111,0...,.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Composite[n_] := FixedPoint[n + 1 + PrimePi[ # ] &, n]; f[n_] := Block[{a = First@Transpose@FactorInteger@n}, a[[ -1]] - a[[1]]]; f[n_] := Block[{a = First@Transpose@FactorInteger@n}, a[[ -1]] - a[[1]]] (* Robert G. Wilson v *)
dif[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]},If[PrimeQ[n],{},Last[ f]- First[f]]]; Flatten[Table[dif[n],{n,4,200}]] (* Harvey P. Dale, May 12 2014 *)

Formula

a(n) = A046665(A002808(n)). - R. J. Mathar, Feb 19 2008

Extensions

More terms from Robert G. Wilson v, Nov 17 2005

Corrected a(19). - Juri-Stepan Gerasimov, Jun 16 2009

a(19)=3 inserted by Klaus Brockhaus, Jun 25 2009