A322866 Lexicographically earliest such sequence a that a(i) = a(j) => A046523(A322863(i)) = A046523(A322863(j)) for all i, j.

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

Offset

1,4

Comments

Restricted growth sequence transform of A046523(A322863(n)).

Equally, restricted growth sequence transform of A278222(A322865(n)).

For all i, j: a(i) = a(j) => A322867(i) = A322867(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
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
A322863(n) = if(!n, 1, A005940(1+A122111(n)));
v322866 = rgs_transform(vector(up_to, n, A046523(A322863(n))));
A322866(n) = v322866[n];

Crossrefs

Cf. A005940, A046523, A122111, A278222, A286622, A322863, A322865, A322867.

Sequence in context: A232396 A270096 A039636 * A328847 A331175 A331954

Adjacent sequences: A322863 A322864 A322865 * A322867 A322868 A322869

Keyword

nonn

Author

Antti Karttunen, Dec 30 2018

Status

approved