A329345 Lexicographically earliest infinite sequence such that a(i) = a(j) => A246277(A329044(i)) = A246277(A329044(j)) for all i, j.

1, 2, 2, 3, 2, 3, 2, 4, 4, 3, 2, 5, 2, 3, 6, 7, 2, 7, 2, 5, 6, 3, 2, 8, 9, 3, 10, 5, 2, 11, 2, 10, 6, 3, 12, 13, 2, 3, 6, 4, 2, 4, 2, 5, 14, 3, 2, 15, 16, 17, 6, 5, 2, 18, 19, 20, 6, 3, 2, 21, 2, 3, 21, 18, 22, 23, 2, 5, 6, 24, 2, 25, 2, 3, 26, 5, 27, 23, 2, 7, 28, 3, 2, 7, 29, 3, 6, 20, 2, 30, 31, 5, 6, 3, 32, 33, 2, 34, 35, 16, 2, 23, 2, 20, 36

Offset

1,2

Comments

Restricted growth sequence transform of function f(n) = A246277(A329044(n)).

For all i, j:

A305800(i) = A305800(j) => a(i) = a(j),

a(i) = a(j) => A329045(i) = A329045(j),

a(i) = a(j) => A329343(i) = A329343(j),

a(i) = a(j) => A329348(i) = A329348(j),

a(i) = a(j) => A329349(i) = A329349(j).

Links

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

Prog

(PARI)
up_to = 1024;
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; };
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A324886(n) = A276086(A108951(n));
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A329044(n) = A064989(A324886(n));
A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f)/2);
v329345 = rgs_transform(vector(up_to, n, A246277(A329044(n))));
A329345(n) = v329345[n];

Crossrefs

Cf. A034386, A064989, A108951, A246277, A276086, A305800, A324886, A329044, A329045, A329343, A329348, A329349.

Cf. also A329048.

Sequence in context: A229123 A173908 A329045 * A054030 A336311 A339874

Adjacent sequences: A329342 A329343 A329344 * A329346 A329347 A329348

Keyword

nonn

Author

Antti Karttunen, Nov 11 2019

Status

approved