A369051 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A085731(i) = A085731(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, 21, 2, 40, 2, 42, 43, 44, 45, 46, 2, 47, 48, 49, 2, 50, 2, 51, 52, 53, 45, 54, 2, 55, 56, 57, 2, 58, 41, 59, 60, 61, 2, 62, 37

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A003415(n), A085731(n)], or equally, of the pair [A003415(n), A083345(n)], or equally, of the pair [A083345(n), A085731(n)].

For all i, j: A369050(i) = A369050(j) => A344025(i) = A344025(j) => a(i) = a(j).

Links

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

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A085731(n) = gcd(A003415(n), n);
Aux369051(n) = [A003415(n), A085731(n)];
v369051 = rgs_transform(vector(up_to, n, Aux369051(n)));
A369051(n) = v369051[n];

Crossrefs

Cf. A003415, A083345, A085731.

Cf. also A344025, A369050.

Sequence in context: A293215 A293232 A300835 * A369046 A344025 A351236

Adjacent sequences: A369048 A369049 A369050 * A369052 A369053 A369054

Keyword

nonn

Author

Antti Karttunen, Jan 15 2024

Status

approved