A336471 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A336158(i) = A336158(j), for all i, j >= 1.

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

Offset

1,3

Comments

Restricted growth sequence transform of the ordered pair [A329697(n), A336158(n)].

For all i, j:

A336470(i) = A336470(j) => a(i) = a(j)

a(i) = a(j) => A336396(i) = A336396(j),

a(i) = a(j) => A336469(i) = A336469(j) => A336477(i) = A336477(j).

This sequence has an ability to see where the terms of A003401 are, as they are the indices of zeros in A336469. Specifically, they are numbers k that satisfy the condition A329697(k) = A001221(A336158(k)), i.e., numbers for which A329697(k) is equal to the number of distinct prime divisors of the odd part of k. See also comments in array A334100.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Prog

(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));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A329697(n) = if(!bitand(n, n-1), 0, 1+A329697(n-(n/vecmax(factor(n)[, 1]))));
Aux336471(n) = [A329697(n), A336158(n)];
v336471 = rgs_transform(vector(up_to, n, Aux336471(n)));
A336471(n) = v336471[n];

Crossrefs

Cf. A000265, A003401, A046523, A329697, A334100, A336158.

Cf. also A003602, A324400, A336159, A336160, A336396, A336469, A336470, A336472, A336473, A336477.

Sequence in context: A349494 A072084 A359587 * A357975 A366605 A133755

Adjacent sequences: A336468 A336469 A336470 * A336472 A336473 A336474

Keyword

nonn

Author

Antti Karttunen, Jul 22 2020

Status

approved