A365466 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336466(A163511(i)) = A336466(A163511(j)) for all i, j >= 1, where A336466 is fully multiplicative with a(p) = oddpart(p-1) for any prime p.

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

Offset

1,7

Comments

Restricted growth sequence transform of the ordered pair [A336466(n), A365426(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));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
A365466aux(n) = [A336466(n), A336466(A163511(n))];
v365466 = rgs_transform(vector(up_to, n, A365466aux(n)));
A365466(n) = v365466[n];

Crossrefs

Cf. A000265, A003602, A163511, A336466, A365426.

Cf. also A365467.

Sequence in context: A014671 A029365 A204178 * A095136 A105540 A356958

Adjacent sequences: A365463 A365464 A365465 * A365467 A365468 A365469

Keyword

nonn

Author

Antti Karttunen, Sep 04 2023

Status

approved