login
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.
2
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 29 2024
STATUS
approved