A329045 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A329044(i)) = A046523(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, 4, 5, 2, 10, 2, 4, 6, 3, 11, 12, 2, 3, 6, 4, 2, 4, 2, 5, 10, 3, 2, 8, 13, 14, 6, 5, 2, 7, 9, 15, 6, 3, 2, 16, 2, 3, 16, 7, 17, 18, 2, 5, 6, 19, 2, 20, 2, 3, 21, 5, 22, 18, 2, 7, 13, 3, 2, 7, 23, 3, 6, 15, 2, 24, 25, 5, 6, 3, 26, 27, 2, 28, 24, 13, 2, 18, 2, 15, 29

Offset

1,2

Comments

Restricted growth sequence transform of function f(n) = A046523(A329044(n)).

For all i, j:

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

a(i) = a(j) => A324888(i) = A324888(j),

a(i) = a(j) => A329046(i) = A329046(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 = 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; };
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));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
v329045 = rgs_transform(vector(up_to, n, A046523(A329044(n))));
A329045(n) = v329045[n];

Crossrefs

Cf. A034386, A064989, A108951, A276086, A305800, A324886, A324888, A329044, A329046.

Cf. also A278226, A286626.

Sequence in context: A308450 A229123 A173908 * A329345 A054030 A336311

Adjacent sequences: A329042 A329043 A329044 * A329046 A329047 A329048

Keyword

nonn

Author

Antti Karttunen, Nov 08 2019

Status

approved