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A374200 a(n) is the minimum value of A347381 that it obtains among the unitary divisors of n larger than 1, where A347381 is the distance from n to the nearest common ancestor of n and sigma(n) in the Doudna-tree (A005940). By convention a(1) = 0.

%I A374200 #17 Jul 24 2024 15:32:46
%S A374200 0,0,1,1,1,0,3,2,2,0,3,1,2,0,1,3,6,0,5,1,1,0,7,1,3,0,3,0,8,0,10,4,1,0,
%T A374200 1,1,4,0,1,1,10,0,9,1,1,0,13,1,4,0,1,1,15,0,1,2,1,0,15,1,7,0,2,5,1,0,
%U A374200 12,1,1,0,19,2,9,0,1,1,3,0,19,1,3,0,20,0,1,0,1,2,22,0,2,1,1,0,1,1,24,0,2,1,20
%N A374200 a(n) is the minimum value of A347381 that it obtains among the unitary divisors of n larger than 1, where A347381 is the distance from n to the nearest common ancestor of n and sigma(n) in the Doudna-tree (A005940). By convention a(1) = 0.
%C A374200 In contrast to A374204 and A374214 it seems that this sequence has no missing values, i.e., it is probably surjective on N.
%H A374200 Antti Karttunen, <a href="/A374200/b374200.txt">Table of n, a(n) for n = 1..100000</a>
%H A374200 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A374200 a(1) = 0, and for n > 1, a(n) = Min_{d|n, d>1, gcd(d,n/d)=1} A347381(d).
%o A374200 (PARI) A374200(n) = { my(m=-1,x); fordiv(n,d,if(d>1 && 1==gcd(d,n/d), x = A347381(d); if(m<0 || x<m, m=x))); if(-1==m,0,m); };
%Y A374200 Cf. A005940, A347381, A347383.
%Y A374200 Cf. also A374204, A374214.
%K A374200 nonn
%O A374200 1,7
%A A374200 _Antti Karttunen_, Jul 09 2024