A378602 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A119347(i) = A119347(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, 10, 6, 6, 2, 11, 3, 6, 5, 12, 2, 13, 2, 14, 6, 6, 6, 15, 2, 6, 6, 16, 2, 17, 2, 18, 19, 6, 2, 20, 3, 18, 6, 18, 2, 21, 6, 21, 6, 6, 2, 22, 2, 6, 23, 24, 6, 25, 2, 18, 6, 26, 2, 27, 2, 6, 18, 18, 6, 28, 2, 29, 8, 6, 2, 30, 6, 6, 6, 31, 2, 32, 6, 18, 6, 6, 6, 33, 2, 18, 23, 34, 2, 28, 2, 35, 36

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A046523(n), A119347(n)].

Links

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

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]); };
A119347(n) = { my(c=[0]); fordiv(n, d, c = Set(concat(c, vector(#c, i, c[i]+d)))); (#c)-1; };
Aux378602(n) = [A046523(n), A119347(n)];
v378602 = rgs_transform(vector(up_to, n, Aux378602(n)));
A378602(n) = v378602[n];

Crossrefs

Cf. A046523, A119347, A101296.

Cf. also A378601, A378603.

Sequence in context: A350068 A378603 A378601 * A300230 A305897 A355834

Adjacent sequences: A378599 A378600 A378601 * A378603 A378604 A378605

Keyword

nonn,new

Author

Antti Karttunen, Dec 01 2024

Status

approved