A356157 -id:A356157 - cp's OEIS frontend

A356307 The nearest common ancestor of A161942(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, 3, 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, 7, 1, 1, 3, 1, 1, 9, 7, 1, 1, 1, 3, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3

Offset: 1

Antti Karttunen, Aug 04 2022

nonn

Cf. A000203, A000265, A161942, A253553, A355931, A356300, A356306, A356307.

Cf. also A356157.

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)));
A356307(n) = A356300sq(A161942(n), gcd(n, A161942(n)));

a(n) = A356300(A161942(n), A355931(n)) = A356300(A161942(n), gcd(n, A161942(n))).

A356156 The nearest common ancestor of n and gcd(n, sigma(n)) in the Doudna tree (A005940).

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 1, 2, 1, 12, 1, 2, 1, 28, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 1, 10, 1, 3, 1, 2, 3, 2, 1, 2, 1, 1, 3, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 1, 1, 1, 3, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 5, 1, 2, 3, 2, 1, 2, 5, 2, 1, 2, 5, 12, 1, 1, 3, 1, 1, 3, 1, 2, 3

Offset: 1

Antti Karttunen, Jul 30 2022

nonn

Cf. A000203, A007691 (fixed points), A009194, A348040, A348041.

Cf. also A347879, A356157, A356158, A356306.

Abincompreflen(n, m) = { my(x=binary(n),y=binary(m),u=min(#x,#y)); for(i=1,u,if(x[i]!=y[i],return(i-1))); (u);};
Abinprefix(n,k) = { my(digs=binary(n)); fromdigits(vector(k,i,digs[i]),2); };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A348040sq(x,y) = Abincompreflen(A156552(x), A156552(y));
A348041sq(x,y) = A005940(1+Abinprefix(A156552(x),A348040sq(x,y)));
A356156(n) = A348041sq(n,gcd(n, sigma(n)));

a(n) = A348041(n, A009194(n)) = A348041(n, gcd(n, A000203(n))).

A356158 a(n) = gcd(n, A347879(n)).

Original entry on oeis.org

1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 3, 1, 1, 3, 2, 1, 2, 1, 10, 1, 2, 1, 6, 1, 1, 1, 28, 1, 2, 1, 2, 3, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 3, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 5, 2, 1, 1, 3, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, 3

Offset: 1

Antti Karttunen, Jul 30 2022

nonn

The fixed points of this sequence is given by the union of {2} and A336702.

Cf. A000203, A336702, A347879, A348040, A348041.

Cf. also A356156, A356157, A356308.

Abincompreflen(n, m) = { my(x=binary(n),y=binary(m),u=min(#x,#y)); for(i=1,u,if(x[i]!=y[i],return(i-1))); (u);};
Abinprefix(n,k) = { my(digs=binary(n)); fromdigits(vector(k,i,digs[i]),2); };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A348040sq(x,y) = Abincompreflen(A156552(x), A156552(y));
A348041sq(x,y) = A005940(1+Abinprefix(A156552(x),A348040sq(x,y)));
A347879(n) = A348041sq(n,sigma(n));
A356158(n) = gcd(n, A347879(n));

a(n) = gcd(n, A347879(n)).

cp's OEIS Frontend

A356307 The nearest common ancestor of A161942(n) and gcd(A000265(n), sigma(n)) in the A253563-tree.

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A356156 The nearest common ancestor of n and gcd(n, sigma(n)) in the Doudna tree (A005940).

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A356158 a(n) = gcd(n, A347879(n)).

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