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A374204 a(n) is the minimum value of A347381 that it obtains among divisors of n larger than 1. By convention a(1) = 0.

%I A374204 #9 Jul 07 2024 17:29:01
%S A374204 0,0,1,0,1,0,3,0,1,0,3,0,2,0,1,0,6,0,5,0,1,0,7,0,1,0,1,0,8,0,10,0,1,0,
%T A374204 1,0,4,0,1,0,10,0,9,0,1,0,13,0,3,0,1,0,15,0,1,0,1,0,15,0,7,0,1,0,1,0,
%U A374204 12,0,1,0,19,0,9,0,1,0,3,0,19,0,1,0,20,0,1,0,1,0,22,0,2,0,1,0,1,0,24,0,1,0,20
%N A374204 a(n) is the minimum value of A347381 that it obtains among divisors of n larger than 1. By convention a(1) = 0.
%H A374204 Antti Karttunen, <a href="/A374204/b374204.txt">Table of n, a(n) for n = 1..100000</a>
%H A374204 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A374204 a(1) = 0, and for n > 1, a(n) = Min_{d|n, d>1} A347381(d).
%F A374204 For nonprime n, a(n) = min(A347381(n), A374214(n)).
%o A374204 (PARI)
%o A374204 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A374204 A252463(n) = if(!(n%2),n/2,A064989(n));
%o A374204 A347381(n) = if(1==n,0, my(lista=List([]), i, k=n, stemvec, stemlen, sbr=sigma(n)); while(k>1, listput(lista,k); k = A252463(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec,sbr))>0, return(stemlen-i)); sbr = A252463(sbr)));
%o A374204 A374204(n) = { my(m=-1,x); fordiv(n,d,if(d>1, x = A347381(d); if(m<0 || x<m, m=x))); if(-1==m,0,m); };
%Y A374204 Cf. A000203, A347381, A374214.
%Y A374204 Cf. also A374196.
%K A374204 nonn
%O A374204 1,7
%A A374204 _Antti Karttunen_, Jul 07 2024