A328388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A327860(i)) = A046523(A327860(j)) for all i, j >= 0.

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

Offset: 0

Author

Antti Karttunen, Oct 15 2019

Keywords

• nonn
• easy
• look

Comments

Restricted growth sequence transform of A046523(A327860(n)).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..30030

Crossrefs

Cf. A003415, A046523, A276086, A327860.

Cf. also A286626 (compare the scatter plots).

Programs

PARI

up_to = 30030;
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; };
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); };
A327860(n) = A003415(A276086(n));
Aux328388(n) = if(!n,0,A046523(A327860(n)));
v328388 = rgs_transform(vector(1+up_to, n, Aux328388(n-1)));
A328388(n) = v328388[1+n];