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.

Previous Showing 11-15 of 15 results.

A337199 Binary weight of A337194(n) = 1+A000265(sigma(n)), where A000265(k) gives the odd part of k.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 3, 1, 4, 2, 1, 1, 4, 3, 1, 2, 3, 2, 2, 1, 1, 4, 5, 2, 3, 3, 1, 2, 1, 2, 4, 1, 3, 1, 1, 3, 1, 3, 2, 2, 1, 1, 2, 2, 3, 3, 4, 1, 2, 1, 3, 2, 5, 5, 1, 3, 1, 3, 2, 1, 4, 4, 5, 1, 3, 1, 2, 1, 1, 3, 4, 2, 5, 3, 3, 3, 4, 1
Offset: 1

Views

Author

Antti Karttunen, Aug 20 2020

Keywords

Links

Crossrefs

Cf. A000120, A000203, A000265, A161942, A336698, A337194.
Cf. also A175548, A336692, A337198.

Programs

Formula

a(n) = A000120(A337194(n)) = A000120(A336698(n)).

A337200 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A337194(i)) = A278222(A337194(j)), for all i, j >= 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 3, 3, 4, 5, 1, 3, 1, 1, 1, 5, 4, 1, 1, 3, 1, 1, 1, 2, 1, 6, 3, 1, 1, 6, 5, 1, 4, 5, 3, 3, 1, 1, 6, 7, 3, 5, 2, 1, 3, 1, 4, 6, 1, 5, 1, 1, 2, 1, 5, 3, 3, 1, 1, 3, 3, 5, 5, 6, 1, 3, 1, 5, 4, 7, 7, 1, 5, 1, 2, 3, 1, 6, 6, 8, 1, 5, 1, 3, 1, 1, 5, 9, 3, 10, 5, 2, 2, 9, 1
Offset: 1

Views

Author

Antti Karttunen, Aug 20 2020

Keywords

Comments

Restricted growth sequence transform of f(n) = A278222(A337194(n)).
For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A337199(i) = A337199(j).

Links

Crossrefs

Cf. A000203, A000265, A278222, A161942, A336698, A337194, A337199.
Cf. also A286622, A324400, A337201.

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));
A337194(n) = (1+A000265(sigma(n)));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
v337200 = rgs_transform(vector(up_to, n, A278222(A337194(n))));
A337200(n) = v337200[n];

A337201 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(A337194(i)) = A278221(A337194(j)), for all i, j >= 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 3, 3, 4, 5, 1, 3, 1, 1, 1, 5, 4, 1, 1, 3, 1, 1, 1, 2, 1, 6, 3, 1, 1, 6, 5, 1, 4, 5, 3, 3, 1, 1, 7, 8, 3, 3, 2, 1, 3, 1, 4, 6, 1, 5, 1, 1, 2, 1, 5, 3, 4, 1, 1, 3, 3, 2, 9, 7, 1, 4, 1, 5, 4, 8, 10, 1, 5, 1, 2, 11, 1, 6, 6, 12, 1, 5, 1, 3, 1, 1, 3, 13, 3, 14, 15, 2, 2, 16, 1
Offset: 1

Views

Author

Antti Karttunen, Aug 20 2020

Keywords

Comments

Restricted growth sequence transform of f(n) = A278221(A337194(n)).
For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A337198(i) = A337198(j).

Links

Crossrefs

Cf. A000203, A000265, A278221, A161942, A336698, A337194, A337198.
Cf. also A286621, A324400, A337200.

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));
A337194(n) = (1+A000265(sigma(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A278221(n) = A046523(A122111(n));
v337201 = rgs_transform(vector(up_to, n, A278221(A337194(n))));
A337201(n) = v337201[n];

A342465 a(n) = A329697(A337194(n)).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 2, 0, 3, 1, 0, 0, 3, 2, 0, 1, 2, 1, 1, 0, 0, 3, 4, 1, 2, 2, 0, 1, 0, 1, 3, 0, 2, 0, 0, 2, 0, 2, 1, 2, 0, 0, 1, 1, 4, 3, 3, 0, 2, 0, 2, 1, 4, 3, 0, 2, 0, 2, 1, 0, 3, 3, 4, 0, 2, 0, 1, 0, 0, 2, 4, 1, 4, 2, 2, 2, 3, 0
Offset: 1

Views

Author

Antti Karttunen, Mar 16 2021

Keywords

Links

Crossrefs

Cf. A000203, A000265, A329697, A337194, A342466.
Cf. also A336694, A336928.

Programs

Formula

a(n) = A329697(A336698(n)) = A329697(A337194(n)).

A342466 a(n) = A336466(1+A000265(sigma(n))), where A336466 is fully multiplicative with a(p) = A000265(p-1) for p prime, and A000265(k) is the odd part of k.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 3, 1, 11, 1, 1, 1, 11, 5, 1, 1, 5, 1, 1, 1, 1, 7, 23, 1, 1, 3, 1, 1, 1, 1, 11, 1, 5, 1, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 9, 9, 7, 1, 1, 1, 5, 1, 23, 15, 1, 5, 1, 3, 1, 1, 11, 11, 29, 1, 5, 1, 1, 1, 1, 1, 21, 1, 27, 3, 3, 3, 13, 1
Offset: 1

Views

Author

Antti Karttunen, Mar 16 2021

Keywords

Links

Crossrefs

Cf. A000203, A000265, A003958, A161942, A337194, A336466, A336698, A342465.

Programs

Formula

a(n) = A336466(A336698(n)) = A336466(A337194(n)).
a(n) = A000265(A003958(1+A161942(n))).
Previous Showing 11-15 of 15 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.