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

%I A328458 #16 Feb 23 2023 15:30:31
%S A328458 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,
%T A328458 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,
%U A328458 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
%N A328458 Maximum run-length of the nontrivial divisors (greater than 1 and less than n) of n.
%C A328458 By convention, a(1) = 1, and a(p) = 0 for p prime.
%H A328458 Antti Karttunen, <a href="/A328458/b328458.txt">Table of n, a(n) for n = 1..100000</a>
%e A328458 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.
%t A328458 Table[Switch[n,1,1,_?PrimeQ,0,_,Max@@Length/@Split[DeleteCases[Divisors[n],1|n],#2==#1+1&]],{n,100}]
%o A328458 (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
%Y A328458 Positions of first appearances are A328459.
%Y A328458 Positions of 0's and 1's are A088723.
%Y A328458 The version that looks at all divisors is A055874.
%Y A328458 The number of successive pairs of divisors > 1 of n is A088722(n).
%Y A328458 The Heinz number of the multiset of run-lengths of divisors of n is A328166(n).
%Y A328458 Cf. A033676, A060681, A060775, A070824, A088725, A129308, A181063, A199970, A328165, A163870, A328194, A328448, A328449.
%K A328458 nonn
%O A328458 1,6
%A A328458 _Gus Wiseman_, Oct 17 2019
%E A328458 Data section extended up to a(105) by _Antti Karttunen_, Feb 23 2023