A328457 Length of the longest run of divisors > 1 of n.

0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 5, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1

Offset: 1

Author

Gus Wiseman, Oct 16 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Records occur at A328448.

Positions of 0's and 1's are A088725.

The version that looks at all divisors (including 1) is A055874.

The number of successive pairs of divisors > 1 of n is A088722(n).

The Heinz number of the multiset of run-lengths of divisors of n is A328166(n).

The longest run of nontrivial divisors of n is A328458(n).

Cf. A000005, A027750, A129308, A181063, A199970, A328162, A328195, A328449, A360128.

Programs

Mathematica

Table[If[n==1,0,Max@@Length/@Split[Rest[Divisors[n]],#2==#1+1&]],{n,100}]

PARI

A328457(n) = { my(rl=0,pd=0,m=0); fordiv(n, d, if(d>1, if(d>(1+pd), m = max(m,rl); rl=0); pd=d; rl++)); max(m,rl); }; \\ Antti Karttunen, Feb 23 2023

Extensions

Data section extended up to a(105) by Antti Karttunen, Feb 23 2023