cp's OEIS Frontend

A356308 a(n) = gcd(n, A356301(n)), where A356301(n) is the nearest common ancestor of A000265(sigma(n)) and A000265(n) in the A253563-tree.

%I A356308 #8 Sep 08 2022 14:06:03
%S A356308 1,1,1,1,1,3,1,1,3,1,1,3,1,1,3,1,1,9,1,1,1,1,1,3,5,1,3,7,1,3,1,1,3,1,
%T A356308 1,3,1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,1,9,1,1,3,1,1,15,1,1,3,1,1,3,1,1,
%U A356308 3,1,1,9,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,45,7,1,1,1,1,3,1,1,9,5,1,3,1,1,3
%N A356308 a(n) = gcd(n, A356301(n)), where A356301(n) is the nearest common ancestor of A000265(sigma(n)) and A000265(n) in the A253563-tree.
%H A356308 Antti Karttunen, <a href="/A356308/b356308.txt">Table of n, a(n) for n = 1..65537</a>
%H A356308 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A356308 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A356308 a(n) = gcd(n, A356301(n)).
%o A356308 (PARI)
%o A356308 A000265(n) = (n>>valuation(n,2));
%o A356308 A161942(n) = A000265(sigma(n));
%o A356308 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 A356308 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 A356308 A356301(n) = A356300sq(A161942(n),A000265(n));
%o A356308 A356308(n) = gcd(n, A356301(n));
%Y A356308 Cf. A000203, A000265, A161942, A253553, A356300, A356301, A356306, A356307.
%Y A356308 Cf. also A356158.
%K A356308 nonn
%O A356308 1,6
%A A356308 _Antti Karttunen_, Aug 04 2022