A356301 The nearest common ancestor of A000265(sigma(n)) and A000265(n) in the tree depicted in A253563.

1, 1, 1, 1, 3, 3, 1, 1, 3, 3, 3, 3, 7, 3, 3, 1, 3, 9, 5, 3, 1, 3, 3, 3, 5, 3, 3, 7, 3, 9, 1, 1, 3, 3, 3, 3, 19, 3, 3, 3, 3, 3, 11, 3, 9, 3, 3, 3, 3, 3, 9, 7, 3, 9, 3, 3, 3, 3, 3, 15, 31, 3, 3, 1, 3, 9, 17, 3, 3, 3, 3, 9, 37, 3, 3, 5, 3, 21, 5, 3, 3, 3, 3, 3, 3, 3, 15, 3, 3, 45, 7, 3, 1, 3, 3, 3, 7, 3, 9, 5, 3, 9, 13, 3, 3

Offset: 1

Author

Antti Karttunen, Aug 03 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed 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, A356300, A356301, A356306, A356307, A356308.

Cf. also A347879.

Positions of 1's in this sequence is given by the union of A000079 and A046528.

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));

Formula

a(n) = A356300(A161942(n), A000265(n)).