A365466 -id:A365466 - cp's OEIS frontend

A365467 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A336467(A163511(i)) = A336467(A163511(j)) for all i, j >= 1, where A336467 is fully multiplicative with a(2) = 1 and a(p) = oddpart(p+1) for odd primes p.

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

Offset: 1

Antti Karttunen, Sep 04 2023

nonn

Restricted growth sequence transform of the ordered pair [A336467(n), A365427(n)].

For all i, j: A003602(i) = A003602(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000265, A003602, A163511, A336467, A365427.

Cf. also A365466.

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));
A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
A365467aux(n) = [A336467(n), A336467(A163511(n))];
v365467 = rgs_transform(vector(up_to,n,A365467aux(n)));
A365467(n) = v365467[n];

A366381 Lexicographically earliest infinite sequence such that a(i) = a(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 p.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 4, 1, 5, 3, 2, 1, 6, 1, 7, 2, 3, 4, 8, 1, 6, 5, 1, 3, 9, 2, 10, 1, 4, 6, 11, 1, 12, 7, 5, 2, 13, 3, 14, 4, 2, 8, 15, 1, 16, 6, 6, 5, 17, 1, 18, 3, 7, 9, 19, 2, 20, 10, 3, 1, 21, 4, 22, 6, 8, 11, 23, 1, 24, 12, 6, 7, 25, 5, 26, 2, 1, 13, 27, 3, 28, 14, 9, 4, 29, 2, 30, 8, 10, 15, 31, 1, 32

Offset: 1

Antti Karttunen, Oct 12 2023

nonn

Restricted growth sequence transform of the ordered pair [A336466(n), A336467(n)].

For all i, j: A003602(i) = A003602(j) => A366380(i) = A366380(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000265, A003602, A336466, A336467, A366380.

Cf. also A365466, A365467.

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));
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])); };
A366381aux(n) = [A336466(n), A336467(n)];
v366381 = rgs_transform(vector(up_to,n,A366381aux(n)));
A366381(n) = v366381[n];

cp's OEIS Frontend

A365467 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A336467(A163511(i)) = A336467(A163511(j)) for all i, j >= 1, where A336467 is fully multiplicative with a(2) = 1 and a(p) = oddpart(p+1) for odd primes p.

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