A329620 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A046523(n), A246277(A324886(n))].

1, 2, 2, 3, 2, 4, 2, 5, 6, 4, 2, 7, 2, 4, 8, 9, 2, 10, 2, 7, 8, 4, 2, 11, 12, 4, 13, 7, 2, 14, 2, 15, 8, 4, 16, 17, 2, 4, 8, 18, 2, 19, 2, 7, 20, 4, 2, 21, 22, 23, 8, 7, 2, 24, 25, 26, 8, 4, 2, 27, 2, 4, 28, 29, 30, 31, 2, 7, 8, 32, 2, 33, 2, 4, 34, 7, 35, 31, 2, 36, 37, 4, 2, 38, 39, 4, 8, 26, 2, 40, 41, 7, 8, 4, 42, 43, 2, 44, 45, 46, 2, 31, 2, 26, 47

Offset: 1

Author

Antti Karttunen, Nov 18 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A046523(n), A246277(A324886(n))].

For all i, j:

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

a(i) = a(j) => A101296(i) = A101296(j),

a(i) = a(j) => A329345(i) = A329345(j),

a(i) = a(j) => A329618(i) = A329618(j),

a(i) = a(j) => A329619(i) = A329619(j).

Links

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

Crossrefs

Cf. A046523, A034386, A108951, A246277, A276086, A305800, A324886, A329345, A329618, A329619.

Programs

PARI

up_to = 8192;
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]); }; \\ From A046523
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));
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);
Aux329620(n) = [A046523(n), A246277(A324886(n))];
v329620 = rgs_transform(vector(up_to, n, Aux329620(n)));
A329620(n) = v329620[n];