A373251 Lexicographically earliest infinite sequence such that a(i) = a(j) => A181819(i) = A181819(j), i mod A181819(i) = j mod 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, 4, 5, 6, 5, 7, 8, 9, 5, 10, 5, 6, 11, 12, 5, 10, 5, 13, 14, 6, 5, 15, 16, 6, 17, 18, 5, 19, 5, 20, 14, 6, 21, 22, 5, 6, 23, 24, 5, 25, 5, 26, 27, 6, 5, 28, 29, 30, 23, 18, 5, 15, 31, 32, 14, 6, 5, 33, 5, 6, 34, 35, 36, 37, 5, 26, 14, 38, 5, 39, 5, 6, 40, 18, 41, 19, 5, 42, 43, 6, 5, 44, 45, 6, 23, 46, 5, 47, 21, 26, 14, 6

Offset: 1

Author

Antti Karttunen, May 30 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the triple [A181819(n), A373247(n), A324198(n)].

For all i, j:

A305900(i) = A305900(j) => a(i) = a(j),

a(i) = a(j) => A373248(i) = A373248(j),

a(i) = a(j) => A373250(i) = A373250(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A101296, A181819, A324198, A373247, A373248, A373250.

Programs

PARI

up_to = 100000;
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); };
Aux373251(n) = [A181819(n), n%A181819(n), A324198(n)];
v373251 = rgs_transform(vector(up_to, n, Aux373251(n)));
A373251(n) = v373251[n];