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A356306 The nearest common ancestor of A000265(n) and gcd(A000265(n), sigma(n)) in the A253563-tree.

%I A356306 #8 Sep 08 2022 14:05:52
%S A356306 1,1,1,1,1,3,1,1,1,1,1,1,1,1,3,1,1,3,1,1,1,1,1,3,1,1,1,7,1,3,1,1,3,1,
%T A356306 1,1,1,1,1,5,1,3,1,1,3,1,1,1,1,1,3,1,1,3,1,1,1,1,1,3,1,1,1,1,1,3,1,1,
%U A356306 3,1,1,3,1,1,1,1,1,3,1,1,1,1,1,3,1,1,3,1,1,9,7,1,1,1,5,3,1,1,3,1,1,3,1,1,3
%N A356306 The nearest common ancestor of A000265(n) and gcd(A000265(n), sigma(n)) in the A253563-tree.
%H A356306 Antti Karttunen, <a href="/A356306/b356306.txt">Table of n, a(n) for n = 1..65537</a>
%H A356306 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A356306 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A356306 a(n) = A356300(A000265(n), A355931(n)).
%o A356306 (PARI)
%o A356306 A000265(n) = (n>>valuation(n,2));
%o A356306 A161942(n) = A000265(sigma(n));
%o A356306 A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
%o A356306 A356300sq(x,y) = if(1==x||1==y,1, my(lista=List([]), i, k=x, stemvec, stemlen, h=y); while(k>1, listput(lista,k); k = A253553(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec,h))>0, return(stemvec[i])); h = A253553(h)));
%o A356306 A356306(n) = A356300sq(A000265(n), gcd(n, A161942(n)));
%Y A356306 Cf. A000203, A000265, A161942, A355931, A356300, A356301, A356307, A356308.
%Y A356306 Cf. also A356156.
%K A356306 nonn
%O A356306 1,6
%A A356306 _Antti Karttunen_, Aug 03 2022