A328396 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = A046523(A276086(A003415(A276086(n)))).

1, 2, 2, 3, 2, 4, 2, 5, 5, 5, 6, 7, 3, 8, 7, 9, 5, 10, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2, 22, 3, 8, 23, 24, 25, 26, 11, 6, 27, 28, 29, 24, 11, 30, 31, 32, 27, 33, 10, 34, 35, 36, 37, 38, 39, 19, 40, 41, 3, 42, 43, 44, 25, 45, 46, 11, 9, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 4, 69, 70, 71, 72, 73, 74, 32

Offset: 0

Author

Antti Karttunen, Oct 15 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of function f(n) = A278226(A327860(n)) = A046523(A276086(A003415(A276086(n)))).

For all i, j: a(i) = a(j) => A328392(i) = A328392(j).

Links

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

Crossrefs

Cf. A003415, A046523, A276086, A327860, A328392.

Cf. also A278226, A286626, A328388, A328395.

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); };
Aux328396(n) = A046523(A276086(A003415(A276086(n))));
v328396 = rgs_transform(vector(1+up_to, n, Aux328396(n-1)));
A328396(n) = v328396[1+n];