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

1,5

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

Prog

(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];

Crossrefs

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

Cf. also A365466, A365467.

Sequence in context: A336812 A281426 A070099 * A126760 A365467 A206437

Adjacent sequences: A366378 A366379 A366380 * A366382 A366383 A366384

Keyword

nonn

Author

Antti Karttunen, Oct 12 2023

Status

approved