A351460 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j), A206787(i) = A206787(j) and A336651(i) = A336651(j) for all i, j >= 1.

1, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 3, 8, 5, 9, 2, 10, 6, 11, 4, 12, 7, 13, 3, 14, 8, 15, 5, 16, 9, 17, 2, 18, 10, 19, 6, 20, 11, 21, 4, 22, 12, 23, 7, 24, 13, 25, 3, 26, 14, 27, 8, 28, 15, 29, 5, 30, 16, 31, 9, 32, 17, 33, 2, 34, 18, 35, 10, 36, 19, 37, 6, 38, 20, 39, 11, 40, 21, 41, 4, 42, 22, 43, 12, 44, 23, 45, 7, 46, 24, 47, 13, 48, 25, 49, 3, 50, 26, 51, 14, 52, 27, 53, 8, 54

Offset: 1

Author

Antti Karttunen, Feb 11 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered triplet [A006530(n), A206787(n), A336651(n)].

For all i, j >= 1:

A324400(i) = A324400(j) => a(i) = a(j),

a(i) = a(j) => A347241(i) = A347241(j),

a(i) = a(j) => A351461(i) = A351461(j) => A347240(i) = A347240(j).

Examples

			a(429) = a(455) because 429 = 3*11*13 and 455 = 5*7*13, so they have equal largest prime factor (A006530), and they also agree on A206787(429) = A206787(455) = 672 and on A336651(429) = A336651(455) = 1 (because both are squarefree), therefore they get equal value (which is 216) allotted to them by the restricted growth sequence transform. - _Antti Karttunen_, Feb 14 2022
		

Links

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

Crossrefs

Cf. A006530, A206787, A336651, A347241, A351461.

Cf. also A324400, A351452.

Differs from A351454 for the first time at n=121, where a(121) = 62, while A351454(121) = 51.

Differs from A103391(1+n) for the first time after n=1 at n=455, where a(455) = 216, while A103391(456) = 229.

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; };
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A206787(n) = sumdiv(n, d, d*(d % 2)*issquarefree(d)); \\ From A206787
A336651(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i,1],1,f[i,1]^(f[i,2]-1))); };
Aux351460(n) = [A006530(n), A206787(n), A336651(n)];
v351460 = rgs_transform(vector(up_to, n, Aux351460(n)));
A351460(n) = v351460[n];