cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Aug 04 2022

Keywords

Links

Crossrefs

Cf. A000203, A000265, A161942, A253553, A355931, A356300, A356306, A356307.
Cf. also A356157.

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

Formula

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

Views

Author

Antti Karttunen, Jul 30 2022

Keywords

Links

Crossrefs

Cf. A000203, A007691 (fixed points), A009194, A348040, A348041.
Cf. also A347879, A356157, A356158, A356306.

Programs

  • PARI
    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)));

Formula

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

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

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Aug 03 2022

Keywords

Links

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)).

A356308 a(n) = gcd(n, A356301(n)), where A356301(n) is the nearest common ancestor of A000265(sigma(n)) and A000265(n) in the A253563-tree.

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 1, 1, 1, 3, 5, 1, 3, 7, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 15, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 45, 7, 1, 1, 1, 1, 3, 1, 1, 9, 5, 1, 3, 1, 1, 3
Offset: 1

Views

Author

Antti Karttunen, Aug 04 2022

Keywords

Links

Crossrefs

Cf. A000203, A000265, A161942, A253553, A356300, A356301, A356306, A356307.
Cf. also A356158.

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));
A356308(n) = gcd(n, A356301(n));

Formula

a(n) = gcd(n, A356301(n)).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.