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%I #9 Feb 23 2023 15:30:26
%S 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,
%T 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,
%U 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
%N Length of the longest run of divisors > 1 of n.
%H Antti Karttunen, <a href="/A328457/b328457.txt">Table of n, a(n) for n = 1..100000</a>
%t Table[If[n==1,0,Max@@Length/@Split[Rest[Divisors[n]],#2==#1+1&]],{n,100}]
%o (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
%Y Records occur at A328448.
%Y Positions of 0's and 1's are A088725.
%Y The version that looks at all divisors (including 1) is A055874.
%Y The number of successive pairs of divisors > 1 of n is A088722(n).
%Y The Heinz number of the multiset of run-lengths of divisors of n is A328166(n).
%Y The longest run of nontrivial divisors of n is A328458(n).
%Y Cf. A000005, A027750, A129308, A181063, A199970, A328162, A328195, A328449, A360128.
%K nonn
%O 1,6
%A _Gus Wiseman_, Oct 16 2019
%E Data section extended up to a(105) by _Antti Karttunen_, Feb 23 2023
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