A356306 - OEIS

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A356306

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

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, 1, 1, 1, 1, 1, 5, 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, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 9, 7, 1, 1, 1, 5, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3

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OFFSET

1,6

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)

FORMULA

a(n) = A356300(A000265(n), A355931(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)));

A356306(n) = A356300sq(A000265(n), gcd(n, A161942(n)));

CROSSREFS

Cf. A000203, A000265, A161942, A355931, A356300, A356301, A356307, A356308.

Cf. also A356156.

Sequence in context: A066715 A082457 A356307 * A355931 A031178 A327401

Adjacent sequences: A356303 A356304 A356305 * A356307 A356308 A356309

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 03 2022

STATUS

approved