A369448 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A327858(i) = A327858(j) and A359589(i) = A359589(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 14, 17, 18, 11, 2, 19, 2, 20, 21, 22, 23, 24, 2, 25, 26, 27, 2, 28, 2, 29, 30, 31, 2, 32, 21, 33, 34, 35, 2, 36, 26, 37, 38, 19, 2, 37, 2, 39, 40, 41, 42, 43, 2, 44, 45, 46, 2, 47, 2, 30, 48, 49, 42, 50, 2, 51, 52, 53, 2, 54, 38, 33, 55

Offset

1,2

Comments

Restricted growth sequence transform of the triplet [A003415(n), A327858(n), A359589(n)].

For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A366297(i) = A366297(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; };
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327858(n) = gcd(A003415(n), A276086(n));
v359589 = DirInverseCorrect(vector(up_to, n, A327858(n)-1));
A359589(n) = v359589[n];
Aux369448(n) = [A003415(n), A327858(n), A359589(n)];
v369448 = rgs_transform(vector(up_to, n, Aux369448(n)));
A369448(n) = v369448[n];

Crossrefs

Cf. A003415, A276086, A305800, A327858, A359589, A359595, A366297.

Cf. also A351236, A369047.

Sequence in context: A373151 A328315 A327970 * A369047 A369040 A328767

Adjacent sequences: A369445 A369446 A369447 * A369449 A369450 A369451

Keyword

nonn

Author

Antti Karttunen, Jan 26 2024

Status

approved