A378605 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001065(i) = A001065(j) and A033630(i) = A033630(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 20, 2, 21, 2, 22, 11, 23, 19, 24, 2, 25, 26, 27, 2, 28, 2, 29, 30, 31, 2, 32, 7, 33, 34, 35, 2, 36, 26, 37, 38, 39, 2, 40, 2, 41, 42, 43, 44, 45, 2, 46, 47, 48, 2, 49, 2, 29, 50, 51, 44, 52, 2, 53, 29, 54, 2, 55, 38, 35, 30, 56, 2, 57, 34, 58, 59, 60, 61, 62, 2, 63, 64, 65, 2, 66, 2, 67, 68

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A001065(n), A033630(n)].

Links

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

Crossrefs

Cf. A001065, A033630.

Cf. also A378603.

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; };
A001065(n) = (sigma(n)-n);
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];
Aux378605(n) = [A001065(n), A033630(n)];
v378605 = rgs_transform(vector(up_to, n, Aux378605(n)));
A378605(n) = v378605[n];