A353520 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A053669(i) = A053669(j), for all i, j >= 1.

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 24, 25, 26, 27, 3, 28, 29, 30, 3, 31, 3, 32, 33, 34, 3, 35, 36, 37, 38, 39, 3, 40, 29, 41, 42, 43, 3, 44, 3, 45, 46, 47, 48, 49, 3, 50, 51, 52, 3, 53, 3, 54, 55, 56, 48, 57, 3, 58, 59, 60, 3, 61, 42, 62, 63, 64, 3, 65, 38

Offset: 1

Author

Antti Karttunen, Apr 25 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of the triplet [A003415(n), A003557(n), A053669(n)].

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j),

a(i) = a(j) => A007814(i) = A007814(j),

a(i) = a(j) => A344025(i) = A344025(j).

Links

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

Crossrefs

Cf. A003415, A003557, A007814, A053669.

Cf. also A305801, A328470, A344025, A351260.

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
A003557(n) = (n/factorback(factorint(n)[, 1]));
A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
Aux353520(n) = [A003415(n), A003557(n), A053669(n)];
v353520 = rgs_transform(vector(up_to,n,Aux353520(n)));
A353520(n) = v353520[n];