A328457 - OEIS

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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

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OFFSET

1,6

LINKS

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

MATHEMATICA

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

PROG

(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

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.

Sequence in context: A069283 A319430 A285337 * A340827 A360119 A033630

Adjacent sequences: A328454 A328455 A328456 * A328458 A328459 A328460

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 16 2019

EXTENSIONS

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

STATUS

approved