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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A366380 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336158(i) = A336158(j), A336466(i) = A336466(j) and A336467(i) = A336467(j) for all i, j >= 1, where A336466 is fully multiplicative with a(p) = oddpart(p-1) for any prime p and A336467 is fully multiplicative with a(2) = 1 and a(p) = oddpart(p+1) for odd primes, and A336158(n) gives the prime signature of the odd part of n.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25, 13, 26, 7, 27, 14, 28, 4, 29, 15, 30, 8, 31, 16, 32, 1, 33, 17, 34, 9, 35, 18, 36, 5, 37, 19, 38, 10, 39, 20, 40, 3, 41, 21, 42, 11, 43, 22, 44, 6, 45, 23, 46, 12, 47, 24, 48, 2, 49, 25, 50
Offset: 1

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Author

Antti Karttunen, Oct 12 2023

Keywords

Comments

Restricted growth sequence transform of the triplet [A336158(n), A336466(n), A336467(n)].
For all i, j >= 1:
A003602(i) = A003602(j) => a(i) = a(j),
a(i) = a(j) => A366381(i) = A366381(j),
a(i) = a(j) => A335880(i) = A335880(j),
a(i) = a(j) => A336390(i) = A336390(j),
a(i) = a(j) => A336470(i) = A336470(j).

Crossrefs

Differs from A003602 and A351090 for the first time at n=153, where a(153) = 38, while A003602(153) = A351090(153) = 77.
Differs from A365388 for the first time at n=99, where a(99) = 50, while A365388(99) = 41.

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
    A336158(n) = A046523(A000265(n));
    A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
    A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
    A366380aux(n) = [A336158(n), A336466(n), A336467(n)];
    v366380 = rgs_transform(vector(up_to,n,A366380aux(n)));
    A366380(n) = v366380[n];
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