A378601 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A083206(i) = A083206(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A046523(n), A083206(n)].

Links

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

Crossrefs

Cf. A046523, A083206, A101296.

Cf. also A378602, A378602, A378603, A378604.

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]); };
v083206 = readvec("b083206_to.txt"); \\ Precomputed with A083206(n) = { my(p=1); fordiv(n, d, p *= ('x^d + 'x^-d)); (polcoeff(p, 0)/2); };
A083206(n) = v083206[n];
Aux378601(n) = [A046523(n), A083206(n)];
v378601 = rgs_transform(vector(up_to, n, Aux378601(n)));
A378601(n) = v378601[n];