A378603 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A033630(i) = A033630(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 3, 6, 2, 7, 2, 6, 6, 8, 2, 7, 2, 9, 6, 6, 2, 10, 3, 6, 5, 9, 2, 11, 2, 12, 6, 6, 6, 13, 2, 6, 6, 14, 2, 15, 2, 16, 16, 6, 2, 17, 3, 16, 6, 16, 2, 14, 6, 18, 6, 6, 2, 19, 2, 6, 16, 20, 6, 15, 2, 16, 6, 21, 2, 22, 2, 6, 16, 16, 6, 23, 2, 24, 8, 6, 2, 25, 6, 6, 6, 26, 2, 27, 6, 16, 6, 6, 6, 28, 2, 16, 16, 29, 2, 23, 2, 26, 21

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A046523(n), A033630(n)].

Links

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

Crossrefs

Cf. A046523, A033630, A101296.

Cf. also A378601, A378602, A378604, A378605.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
v033630 = readvec("b033630_to.txt"); \\ Precomputed with A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
A033630(n) = v033630[n];
Aux378603(n) = [A046523(n), A033630(n)];
v378603 = rgs_transform(vector(up_to, n, Aux378603(n)));
A378603(n) = v378603[n];