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A356301
The nearest common ancestor of A000265(sigma(n)) and A000265(n) in the tree depicted in A253563.
4
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
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. 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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 03 2022
STATUS
approved