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.

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

Author

Antti Karttunen, Oct 12 2023

Keywords

• nonn

Comments

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).

Links

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

Crossrefs

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

Cf. also A365466, 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));
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];