A374033 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278226(A373985(i)) = A278226(A373985(j)), for all i, j >= 1.

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

Offset

1,4

Comments

Restricted growth sequence transform of A278226(A373985(n)).

For all i, j >= 1:

A305800(i) = A305800(j) => a(i) = a(j) => A373989(i) = A373989(j).

Links

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

Index entries for sequences related to primorial numbers

Prog

(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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A278226(n) = A046523(A276086(n));
A373985(n) = { my(f=factor(n), m=1, s=0); for(i=1, #f~, my(x=prod(i=1, primepi(f[i, 1]), prime(i))); s += f[i, 2]*x; m *= x^f[i, 2]); gcd(m, s); };
v374033 = rgs_transform(vector(up_to, n, A278226(A373985(n))));
A374033(n) = v374033[n];

Crossrefs

Cf. A002110, A046523, A108951, A276086, A278226, A373158, A373985.

Cf. A305800, A373989.

Cf. also A373982, A373983, A374032.

Sequence in context: A192013 A373989 A329618 * A026517 A072047 A327521

Adjacent sequences: A374030 A374031 A374032 * A374034 A374035 A374036

Keyword

nonn

Author

Antti Karttunen, Jun 27 2024

Status

approved