A325384 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = [A000203(n), A009194(n)] for all other numbers, except f(p) = 0 for odd primes.

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 12, 14, 18, 19, 3, 20, 3, 21, 22, 23, 24, 25, 3, 26, 27, 28, 3, 29, 3, 30, 31, 32, 3, 33, 34, 35, 36, 37, 3, 38, 39, 40, 41, 42, 3, 43, 3, 44, 45, 46, 47, 48, 3, 49, 50, 51, 3, 52, 3, 53, 54, 55, 56, 57, 3, 58, 59, 49, 3, 60, 61, 62, 63, 64, 3, 65, 66, 67, 68, 51, 69, 70, 3, 71

Offset: 1

Author

Antti Karttunen, May 08 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A000203, A009194, A300230, A305801, A325382, A325383.

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; };
A009194(n) = gcd(n,sigma(n));
Aux325384(n) = if((n%2)&&isprime(n),0,[sigma(n),A009194(n)]);
v325384 = rgs_transform(vector(up_to,n,Aux325384(n)));
A325384(n) = v325384[n];