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

1,5

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

Formula

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

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 *)

Crossrefs

Sequence in context: A232101 A176249 A083722 * A100576 A212332 A371750

Adjacent sequences: A111423 A111424 A111425 * A111427 A111428 A111429

Keyword

nonn

Author

Giovanni Teofilatto, Nov 13 2005

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

Status

approved