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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Aug 04 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A000265, A161942, A253553, A356300, A356301, A356306, A356307.

Cf. also A356158.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A161942(n) = A000265(sigma(n));
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));
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)));
A356301(n) = A356300sq(A161942(n),A000265(n));
A356308(n) = gcd(n, A356301(n));

Formula

a(n) = gcd(n, A356301(n)).