A320012 Filter sequence combined from those proper divisors d of n for which 2 == d (mod 3); Restricted growth sequence transform of A319992.

1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 4, 5, 1, 2, 1, 3, 1, 6, 1, 5, 4, 2, 1, 7, 1, 3, 1, 5, 8, 9, 4, 2, 1, 2, 1, 10, 1, 7, 1, 6, 4, 11, 1, 5, 1, 3, 12, 13, 1, 2, 14, 15, 1, 16, 1, 17, 1, 2, 1, 18, 4, 6, 1, 9, 19, 20, 1, 5, 1, 2, 4, 21, 8, 13, 1, 10, 1, 22, 1, 7, 23, 2, 24, 25, 1, 3, 1, 11, 1, 26, 4, 18, 1, 7, 8, 27, 1, 9, 1, 28, 29

Offset

1,4

Comments

For all i, j:

a(i) = a(j) => A320005(i) = A320005(j),

a(i) = a(j) => A293898(i) = A293898(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; };
A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A319992(n) = { my(m=1); fordiv(n, d, if((d<n)&&(2==(d%3)), m *= A019565(d))); m; };
v320012 = rgs_transform(vector(up_to, n, A319992(n)));
A320012(n) = v320012[n];

Crossrefs

Cf. A293224, A319992, A320010, A320011, A320013, A320014.

Sequence in context: A087942 A359237 A327925 * A359508 A352825 A241276

Adjacent sequences: A320009 A320010 A320011 * A320013 A320014 A320015

Keyword

nonn

Author

Antti Karttunen, Oct 03 2018

Status

approved