A356307 - OEIS

%I #10 Sep 08 2022 14:05:58

%S 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 1,1,1,1,1,3,1,3,1,1,3,1,1,1,1,1,3,1,1,3,1,1,1,1,1,3,1,1,1,1,1,3,1,1,

%U 3,1,1,3,1,1,1,1,1,3,1,1,1,1,1,7,1,1,3,1,1,9,7,1,1,1,3,3,1,1,3,1,1,3,1,1,3

%N The nearest common ancestor of A161942(n) and gcd(A000265(n), sigma(n)) in the A253563-tree.

%H Antti Karttunen, <a href="/A356307/b356307.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A356300(A161942(n), A355931(n)) = A356300(A161942(n), gcd(n, A161942(n))).

%o (PARI)

%o A000265(n) = (n>>valuation(n,2));

%o A161942(n) = A000265(sigma(n));

%o 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 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 A356307(n) = A356300sq(A161942(n), gcd(n, A161942(n)));

%Y Cf. A000203, A000265, A161942, A253553, A355931, A356300, A356306, A356307.

%Y Cf. also A356157.

%K nonn

%O 1,6

%A _Antti Karttunen_, Aug 04 2022