A337201 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(A337194(i)) = A278221(A337194(j)), for all i, j >= 1.

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 3, 3, 4, 5, 1, 3, 1, 1, 1, 5, 4, 1, 1, 3, 1, 1, 1, 2, 1, 6, 3, 1, 1, 6, 5, 1, 4, 5, 3, 3, 1, 1, 7, 8, 3, 3, 2, 1, 3, 1, 4, 6, 1, 5, 1, 1, 2, 1, 5, 3, 4, 1, 1, 3, 3, 2, 9, 7, 1, 4, 1, 5, 4, 8, 10, 1, 5, 1, 2, 11, 1, 6, 6, 12, 1, 5, 1, 3, 1, 1, 3, 13, 3, 14, 15, 2, 2, 16, 1

Offset: 1

Author

Antti Karttunen, Aug 20 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of f(n) = A278221(A337194(n)).

For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A337198(i) = A337198(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A000265, A278221, A161942, A336698, A337194, A337198.

Cf. also A286621, A324400, A337200.

Programs

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));
A337194(n) = (1+A000265(sigma(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A278221(n) = A046523(A122111(n));
v337201 = rgs_transform(vector(up_to, n, A278221(A337194(n))));
A337201(n) = v337201[n];