A319348 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j) and A051953(i) = A051953(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 30, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 47, 2, 50, 2, 51, 52, 53, 46, 54, 2, 55, 56, 57, 2, 58, 41, 59, 60, 61, 2, 62, 37, 63, 64, 65, 66, 67, 2, 68, 69, 70, 2

Offset: 1

Author

Antti Karttunen, Sep 29 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of ordered pair [A003557(n), A051953(n)].

For all i, j: a(i) = a(j) => A318305(i) = A318305(j).

Links

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

Crossrefs

Cf. A003557, A051953, A319349.

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; };
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
A051953(n) = (n-eulerphi(n));
v319348 = rgs_transform(vector(up_to,n,[A003557(n),A051953(n)]));
A319348(n) = v319348[n];

Formula

For n >= 3, a(n) = A319349(n) - 1.

Extensions

Name changed by Antti Karttunen, Feb 03 2024