A100387 a(n) is the largest number x such that for m=n to n+x-1, A006530(m) decreases.

1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 3, 2, 1, 4, 3, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 1, 3, 2, 1, 2, 1, 1, 1, 1, 3, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1

Offset

2,2

Comments

A006530(m) is the largest prime factor of m.

Links

Table of n, a(n) for n=2..105.

Formula

From Pontus von Brömssen, Nov 09 2022: (Start)

a(n) = 1 if and only if n >= 2 and n is a term of A070089.

If a(n) > 1 then a(n) = a(n+1)+1.

(End)

Example

a(13)=4 because the largest prime factors of 13,14,15,16 are 13,7,5,2; but A006530(17)=17.

Mathematica

<<NumberTheory`NumberTheoryFunctions` mxp[x_] :=Max[PrimeFactorList[x]]; uph=Table[First[Flatten[Position[Sign[RotateLeft[Table[mxp[n+j], {j, 0, 15}]]-Table[mxp[n+j], {j, 0, 15}]], 1]]], {n, 1, 256}]

Crossrefs

Cf. A006530, A070087, A070089, A071870, A079748, A100376, A100385, A100386.

Sequence in context: A023520 A103587 A306446 * A322869 A229344 A210501

Adjacent sequences: A100384 A100385 A100386 * A100388 A100389 A100390

Keyword

nonn

Author

Labos Elemer, Dec 10 2004

Extensions

Edited by Don Reble, Jun 13 2007

Status

approved