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A320013 Filter sequence constructed from the binary expansions of those proper divisors of n that are not multiples of 3. 4
1, 2, 2, 3, 2, 3, 2, 4, 2, 5, 2, 4, 2, 6, 7, 8, 2, 3, 2, 9, 10, 11, 2, 8, 7, 12, 2, 13, 2, 14, 2, 15, 16, 17, 18, 4, 2, 19, 20, 21, 2, 22, 2, 23, 7, 24, 2, 15, 10, 25, 26, 27, 2, 3, 28, 29, 30, 31, 2, 32, 2, 33, 10, 34, 35, 36, 2, 37, 38, 39, 2, 8, 2, 40, 41, 42, 43, 44, 2, 45, 2, 46, 2, 47, 48, 49, 50, 51, 2, 14, 52, 53, 54, 55, 56, 34, 2, 57, 16, 58, 2, 59, 2, 60, 61 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Restricted growth sequence transform of ordered pair [A319991(n), A319992(n)].

For all i, j: a(i) = a(j) => A320015(i) = A320015(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

A319991(n) = { my(m=1); fordiv(n, d, if((d<n)&&(1==(d%3)), m *= A019565(d))); m; };

A319992(n) = { my(m=1); fordiv(n, d, if((d<n)&&(2==(d%3)), m *= A019565(d))); m; };

v320013 = rgs_transform(vector(up_to, n, [A319991(n), A319992(n)]));

A320013(n) = v320013[n];

CROSSREFS

Cf. A019565, A319991, A319992, A320011, A320012, A320014.

Cf. also A293226, A300833.

Sequence in context: A087458 A052180 A065151 * A299990 A175193 A073093

Adjacent sequences:  A320010 A320011 A320012 * A320014 A320015 A320016

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 03 2018

STATUS

approved

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)