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.

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A335425 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000188(i) = A000188(j) and A335424(i) = A335424(j) for all i, j >= 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 13 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A000188(n), A046523(A335423(n))].
For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A001222(i) = A001222(j).

Crossrefs

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; };
    A000188(n) = core(n, 1)[2]; \\ From A000188
    A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
    A248663(n) = A048675(core(n));
    A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
    A335423(n) = A005940(1+A248663(n));
    A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
    Aux335425(n) = [A000188(n),A046523(A335423(n))];
    v335425 = rgs_transform(vector(up_to,n,Aux335425(n)));
    A335425(n) = v335425[n];

A335423 a(n) = A005940(1+A248663(n)).

Original entry on oeis.org

1, 2, 3, 1, 5, 4, 7, 2, 1, 6, 11, 3, 13, 10, 9, 1, 17, 2, 19, 5, 15, 14, 23, 4, 1, 22, 3, 7, 29, 8, 31, 2, 21, 26, 25, 1, 37, 34, 33, 6, 41, 12, 43, 11, 5, 38, 47, 3, 1, 2, 39, 13, 53, 4, 35, 10, 51, 46, 59, 9, 61, 58, 7, 1, 55, 20, 67, 17, 57, 18, 71, 2, 73, 62, 3, 19, 49, 28, 79, 5, 1, 74, 83, 15, 65, 82, 69, 14, 89, 6
Offset: 1

Views

Author

Antti Karttunen, Jun 13 2020

Keywords

Crossrefs

Programs

  • PARI
    A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
    A248663(n) = A048675(core(n));
    A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
    A335423(n) = A005940(1+A248663(n));

Formula

a(n) = A005940(1+A248663(n)) = A005940(1+A048675(A007913(n))).
Showing 1-2 of 2 results.