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

1,5

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)

Formula

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

Prog

(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));

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.

Sequence in context: A338696 A301303 A285116 * A349813 A266529 A266509

Adjacent sequences: A356298 A356299 A356300 * A356302 A356303 A356304

Keyword

nonn

Author

Antti Karttunen, Aug 03 2022

Status

approved