A355000 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A327858(i) = A327858(j) for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Jul 19 2022

Keywords

• nonn
• easy

Comments

Restricted growth sequence transform of the ordered pair [A046523(n), A327858(n)].

For all i, j: A351235(i) = A351235(j) => a(i) = a(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A046523, A276086, A327858, A351235.

Cf. also A355830, A355831, A355836.

Programs

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; };
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327858(n) = gcd(A003415(n),A276086(n));
Aux355000(n) = [A046523(n), A327858(n)];
v355000 = rgs_transform(vector(up_to,n,Aux355000(n)));
A355000(n) = v355000[n];