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A324389
Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A009194(n), A318458(n)] for all other numbers, except f(1) = -1.
6
1, 2, 3, 2, 3, 4, 3, 2, 2, 5, 3, 6, 3, 7, 8, 2, 3, 9, 3, 10, 3, 11, 3, 12, 2, 13, 14, 15, 3, 16, 3, 2, 17, 18, 3, 19, 3, 11, 3, 20, 3, 21, 3, 22, 23, 7, 3, 6, 2, 24, 25, 26, 3, 27, 28, 29, 28, 30, 3, 31, 3, 32, 33, 2, 3, 34, 3, 18, 17, 35, 3, 36, 3, 5, 3, 37, 3, 38, 3, 39, 2, 18, 3, 40, 41, 11, 17, 42, 3, 43, 44, 45, 3, 46, 47, 12, 3, 48, 23, 49, 3, 50, 3
OFFSET
1,2
COMMENTS
For all i, j:
A324401(i) = A324401(j) => a(i) = a(j).
Regarding the scatter plot of this sequence, see also comments in A318310. - Antti Karttunen, Feb 04 2020
PROG
(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));
A318458(n) = bitand(n, sigma(n)-n);
Aux324389(n) = if(1==n, -1, [A009194(n), A318458(n)]);
v324389 = rgs_transform(vector(up_to, n, Aux324389(n)));
A324389(n) = v324389[n];
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Mar 05 2019
STATUS
approved