

A328458


Maximum runlength of the nontrivial divisors (greater than 1 and less than n) of n.


2



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

1,6


COMMENTS

By convention, a(1) = 1, and a(p) = 0 for p prime.


LINKS

Table of n, a(n) for n=1..87.


EXAMPLE

The nonsingleton runs of the nontrivial divisors of 1260 are: {2,3,4,5,6,7} {9,10} {14,15} {20,21} {35,36}, so a(1260) = 6.


MATHEMATICA

Table[Switch[n, 1, 1, _?PrimeQ, 0, _, Max@@Length/@Split[DeleteCases[Divisors[n], 1n], #2==#1+1&]], {n, 100}]


CROSSREFS

Positions of first appearances are A328459.
Positions of 0's and 1's are A088723.
The version that looks at all divisors is A055874.
The number of successive pairs of divisors > 1 of n is A088722(n).
The Heinz number of the multiset of runlengths of divisors of n is A328166(n).
Cf. A033676, A060681, A060775, A070824, A088725, A129308, A181063, A199970, A328165, A163870, A328194, A328448, A328449.
Sequence in context: A034178 A317531 A074169 * A099362 A321378 A307039
Adjacent sequences: A328455 A328456 A328457 * A328459 A328460 A328461


KEYWORD

nonn


AUTHOR

Gus Wiseman, Oct 17 2019


STATUS

approved



