A322861 Lexicographically earliest such sequence a that a(i) = a(j) => A278222(A285330(i)) = A278222(A285330(j)) for all i, j.

1, 2, 2, 2, 2, 3, 2, 2, 3, 4, 2, 3, 2, 4, 3, 2, 2, 3, 2, 4, 4, 4, 2, 4, 4, 4, 4, 5, 2, 5, 2, 2, 4, 4, 3, 3, 2, 4, 4, 4, 2, 6, 2, 6, 7, 4, 2, 4, 5, 4, 4, 6, 2, 3, 4, 5, 4, 4, 2, 7, 2, 4, 8, 2, 4, 6, 2, 4, 4, 6, 2, 9, 2, 4, 10, 6, 3, 6, 2, 6, 9, 4, 2, 8, 4, 4, 4, 6, 2, 7, 4, 11, 4, 4, 4, 4, 2, 5, 4, 4, 2, 6, 2, 6, 5

Offset: 1

Author

Antti Karttunen, Dec 31 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A278222(A285330(n)).

For all i, j:

A322806(i) = A322806(j) => a(i) = a(j),

A322807(i) = A322807(j) => a(i) = a(j),

a(i) = a(j) => A322862(i) = A322862(j).

Links

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

Crossrefs

Cf. A048675, A278222, A285330, A286622, A322806, A322807, A322862, A322868.

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ From A048675
A285328(n) = { my(r); if((n > 1 && !bitand(n,(n-1))), (n/2), r=A007947(n); if(r==n,1,n = n-r; while(A007947(n) <> r, n = n-r); n)); };
A285330(n) = if(moebius(n)<>0,A048675(n),A285328(n));
A278222(n) = A046523(A005940(1+n));
v322861 = rgs_transform(vector(up_to,n,A278222(A285330(n))));
A322861(n) = v322861[n];