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a(n) is the largest number x such that for m=n to n+x-1, A006530(m) decreases.
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%I #9 Nov 09 2022 19:08:42

%S 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,

%T 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,

%U 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

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

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

%F From _Pontus von Brömssen_, Nov 09 2022: (Start)

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

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

%F (End)

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

%t <<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}]

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

%K nonn

%O 2,2

%A _Labos Elemer_, Dec 10 2004

%E Edited by _Don Reble_, Jun 13 2007