A355831 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A354347(i) = A354347(j) for all i, j >= 1.

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

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A046523(n), A354347(n)].

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]));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A345000(n) = gcd(A003415(n), A003415(A276086(n)));
v354347 = DirInverseCorrect(vector(up_to, n, A345000(n)));
A354347(n) = v354347[n];
Aux355831(n) = [A046523(n), A354347(n)];
v355831 = rgs_transform(vector(up_to, n, Aux355831(n)));
A355831(n) = v355831[n];

Crossrefs

Cf. A305800, A355830, A355832.

Sequence in context: A305790 A294877 A355830 * A300223 A351949 A300226

Adjacent sequences: A355828 A355829 A355830 * A355832 A355833 A355834

Keyword

nonn

Author

Antti Karttunen, Jul 20 2022

Status

approved