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

1,5

Comments

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

For all i, j: A003602(i) = A003602(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));
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];

Crossrefs

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

Cf. also A365466.

Sequence in context: A070099 A366381 A126760 * A206437 A296085 A353644

Adjacent sequences: A365464 A365465 A365466 * A365468 A365469 A365470

Keyword

nonn

Author

Antti Karttunen, Sep 04 2023

Status

approved