A322868 Lexicographically earliest such sequence a that a(i) = a(j) => A278222(A048675(i)) = A278222(A048675(j)) for all i, j.

1, 2, 2, 2, 2, 3, 2, 3, 2, 4, 2, 2, 2, 4, 3, 2, 2, 4, 2, 3, 4, 4, 2, 4, 2, 4, 3, 4, 2, 5, 2, 4, 4, 4, 3, 3, 2, 4, 4, 5, 2, 6, 2, 4, 2, 4, 2, 3, 2, 4, 4, 4, 2, 5, 4, 6, 4, 4, 2, 2, 2, 4, 3, 3, 4, 6, 2, 4, 4, 6, 2, 5, 2, 4, 4, 4, 3, 6, 2, 2, 2, 4, 2, 3, 4, 4, 4, 6, 2, 4, 4, 4, 4, 4, 4, 5, 2, 4, 4, 4, 2, 6, 2, 6, 5

Offset

1,2

Comments

Restricted growth sequence transform of A278222(A048675(n)), or equivalently, of A278222(A322821(n)).

For all i, j: a(i) = a(j) => A322869(i) = A322869(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

Prog

(PARI)
up_to = 8192;
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 };
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
A278222(n) = A046523(A005940(1+n));
v322868 = rgs_transform(vector(up_to, n, A278222(A048675(n))));
A322868(n) = v322868[n];

Crossrefs

Cf. A005940, A046523, A048675, A278222, A322821, A322861, A322869.

Sequence in context: A341829 A344888 A216325 * A240975 A242166 A068211

Adjacent sequences: A322865 A322866 A322867 * A322869 A322870 A322871

Keyword

nonn

Author

Antti Karttunen, Dec 31 2018

Status

approved