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.

A365394 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A365426(i) = A365426(j) for all i, j >= 0.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 5, 2, 6, 1, 7, 4, 4, 3, 8, 3, 9, 2, 8, 5, 10, 2, 10, 6, 11, 1, 12, 7, 7, 4, 13, 4, 14, 3, 15, 8, 16, 3, 16, 9, 17, 2, 13, 8, 18, 5, 19, 10, 20, 2, 18, 10, 21, 6, 21, 11, 6, 1, 22, 12, 12, 7, 23, 7, 24, 4, 25, 13, 26, 4, 26, 14, 27, 3, 25, 15, 28, 8, 29, 16, 30, 3, 28, 16, 31, 9, 31, 17
Offset: 0

Views

Author

Antti Karttunen, Sep 04 2023

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A365425(n), A365426(n)].
Restricted growth sequence transform of the function f(n) = A336470(A163511(n)).
For all i, j: a(i) = a(j) => A334204(i) = A334204(j).

Links

Crossrefs

Cf. A000265, A003602, A046523, A163511, A336470, A365425, A365426.
Cf. also A350067, A365395, A366792 (compare the scatter plots).

Programs

  • PARI
    up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A365425(n) = A046523(A000265(A163511(n)));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
A365426(n) = A336466(A163511(n));
A365394aux(n) = [A365425(n), A365426(n)];
v365394 = rgs_transform(vector(1+up_to,n,A365394aux(n-1)));
A365394(n) = v365394[1+n];

Formula

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

A365427 a(n) = A336467(A163511(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 9, 1, 3, 3, 1, 1, 1, 1, 27, 1, 9, 9, 1, 1, 3, 3, 3, 3, 1, 1, 3, 1, 1, 1, 81, 1, 27, 27, 1, 1, 9, 9, 3, 9, 1, 1, 9, 1, 3, 3, 9, 3, 3, 3, 3, 3, 1, 1, 9, 1, 3, 3, 7, 1, 1, 1, 243, 1, 81, 81, 1, 1, 27, 27, 3, 27, 1, 1, 27, 1, 9, 9, 9, 9, 3, 3, 9, 9, 1, 1, 27, 1, 9, 9, 49, 1, 3, 3, 27, 3
Offset: 0

Views

Author

Antti Karttunen, Sep 03 2023

Keywords

Links

Crossrefs

Cf. A000265, A163511, A336467.
Cf. also A365426.

Programs

  • PARI
    A000265(n) = (n>>valuation(n,2));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
A365427(n) = A336467(A163511(n));

Formula

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

A365466 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336466(A163511(i)) = A336466(A163511(j)) for all i, j >= 1, where A336466 is fully multiplicative with a(p) = oddpart(p-1) for any prime p.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 2, 4, 1, 1, 1, 5, 1, 2, 3, 6, 1, 1, 2, 4, 2, 7, 4, 8, 1, 3, 1, 2, 1, 5, 5, 9, 1, 3, 2, 10, 3, 11, 6, 12, 1, 5, 1, 4, 2, 13, 4, 14, 2, 15, 7, 16, 4, 8, 8, 17, 1, 2, 3, 18, 1, 19, 2, 20, 1, 5, 5, 21, 5, 22, 9, 23, 1, 1, 3, 24, 2, 11, 10, 25, 3, 6, 11, 26, 6, 27, 12, 28, 1, 2, 5
Offset: 1

Views

Author

Antti Karttunen, Sep 04 2023

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A336466(n), A365426(n)].
For all i, j: A003602(i) = A003602(j) => a(i) = a(j).

Links

Crossrefs

Cf. A000265, A003602, A163511, A336466, A365426.
Cf. also A365467.

Programs

  • PARI
    up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A000265(n) = (n>>valuation(n,2));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
A365466aux(n) = [A336466(n), A336466(A163511(n))];
v365466 = rgs_transform(vector(up_to,n,A365466aux(n)));
A365466(n) = v365466[n];

A366787 a(n) = A366789(A163511(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 9, 1, 3, 3, 1, 1, 1, 1, 27, 1, 9, 9, 1, 1, 3, 3, 3, 3, 1, 1, 5, 1, 1, 1, 81, 1, 27, 27, 1, 1, 9, 9, 3, 9, 1, 1, 25, 1, 3, 3, 9, 3, 3, 3, 5, 3, 1, 1, 15, 1, 5, 5, 3, 1, 1, 1, 243, 1, 81, 81, 1, 1, 27, 27, 3, 27, 1, 1, 125, 1, 9, 9, 9, 9, 3, 3, 25, 9, 1, 1, 75, 1, 25, 25, 9, 1, 3, 3, 27
Offset: 0

Views

Author

Antti Karttunen, Oct 23 2023

Keywords

Links

Crossrefs

Cf. A163511, A366789, A366792.
Cf. also A365426, A365427

Programs

  • PARI
    A000265(n) = (n>>valuation(n,2));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A366789(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(primepi(f[k, 1]))^f[k, 2]); };
A366787(n) = A366789(A163511(n));
Showing 1-4 of 4 results.

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