A331174 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = min(n, A122111(n)), for all other n, except for odd primes p, f(p) = 0.

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

Offset: 1

Author

Antti Karttunen, Jan 15 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of function f(n) = 0 if n is an odd prime, otherwise f(n) = A331170(n).

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j) => A001221(i) = A001221(j).

Links

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

Crossrefs

Cf. A001221, A064989, A122111, A305801, A331170.

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; };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
Aux331174(n) = if((n%2)&&isprime(n),0,min(n, A122111(n)));
v331174 = rgs_transform(vector(up_to, n, Aux331174(n)));
A331174(n) = v331174[n];