A328458 Maximum run-length of the nontrivial divisors (greater than 1 and less than n) of n.

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

Offset

1,6

Comments

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

Links

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

Example

The non-singleton 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], 1|n], #2==#1+1&]], {n, 100}]

Prog

(PARI) A328458(n) = if(1==n, n, my(rl=0, pd=0, m=0); fordiv(n, d, if(1<d && d<n, if(d>(1+pd), m = max(m, rl); rl=0); pd=d; rl++)); max(m, rl)); \\ Antti Karttunen, Feb 23 2023

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 run-lengths of divisors of n is A328166(n).

Cf. A033676, A060681, A060775, A070824, A088725, A129308, A181063, A199970, A328165, A163870, A328194, A328448, A328449.

Sequence in context: A317531 A074169 A363859 * A099362 A321378 A307039

Adjacent sequences: A328455 A328456 A328457 * A328459 A328460 A328461

Keyword

nonn

Author

Gus Wiseman, Oct 17 2019

Extensions

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

Status

approved