A373248 Lexicographically earliest infinite sequence such that a(i) = a(j) => gcd(i,A181819(i)) = gcd(j,A181819(j)) and gcd(i,A276086(i)) = gcd(j,A276086(j)), for all i, j >= 1, where A181819 is the prime shadow of n, and A276086 is the primorial base exp-function.

1, 2, 3, 1, 1, 2, 1, 1, 4, 5, 1, 6, 1, 2, 7, 1, 1, 6, 1, 5, 3, 2, 1, 2, 8, 2, 3, 2, 1, 2, 1, 1, 3, 2, 9, 10, 1, 2, 3, 11, 1, 12, 1, 2, 13, 2, 1, 2, 9, 14, 3, 2, 1, 2, 15, 12, 3, 2, 1, 16, 1, 2, 17, 1, 1, 2, 1, 2, 3, 18, 1, 19, 1, 2, 20, 2, 9, 2, 1, 5, 3, 2, 1, 21, 15, 2, 3, 2, 1, 6, 9, 2, 3, 2, 1, 2, 1, 22, 4, 15

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A324198(n), A373246(n)].

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; };
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
A324198(n) = { my(m=1, p=2, orgn=n); while(n, m *= (p^min(n%p, valuation(orgn, p))); n = n\p; p = nextprime(1+p)); (m); };
Aux373248(n) = [gcd(n, A181819(n)), A324198(n)];
v373248 = rgs_transform(vector(up_to, n, Aux373248(n)));
A373248(n) = v373248[n];

Crossrefs

Cf. A181819, A276086, A324198, A373246.

Sequence in context: A030413 A139434 A113925 * A328231 A180466 A105083

Adjacent sequences: A373245 A373246 A373247 * A373249 A373250 A373251

Keyword

nonn

Author

Antti Karttunen, May 29 2024

Status

approved