A335424 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A335423(i)) = A046523(A335423(j)) for all i, j >= 1.

1, 2, 2, 1, 2, 3, 2, 2, 1, 4, 2, 2, 2, 4, 3, 1, 2, 2, 2, 2, 4, 4, 2, 3, 1, 4, 2, 2, 2, 5, 2, 2, 4, 4, 3, 1, 2, 4, 4, 4, 2, 6, 2, 2, 2, 4, 2, 2, 1, 2, 4, 2, 2, 3, 4, 4, 4, 4, 2, 3, 2, 4, 2, 1, 4, 6, 2, 2, 4, 6, 2, 2, 2, 4, 2, 2, 3, 6, 2, 2, 1, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 3, 2, 2, 2, 1, 2, 6, 2, 4, 5

Offset

1,2

Comments

For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A162642(i) = A162642(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Prog

(PARI)
up_to = 65537;
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; };
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A248663(n) = A048675(core(n));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A335423(n) = A005940(1+A248663(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
v335424 = rgs_transform(vector(up_to, n, A046523(A335423(n))));
A335424(n) = v335424[n];

Crossrefs

Cf. A046523, A162642, A248663, A335423, A335425.

Cf. also A286622, A305800.

Sequence in context: A056173 A216817 A263765 * A270073 A027348 A238325

Adjacent sequences: A335421 A335422 A335423 * A335425 A335426 A335427

Keyword

nonn

Author

Antti Karttunen, Jun 13 2020

Status

approved