A320013 - OEIS

A320013

Filter sequence constructed from the binary expansions of those proper divisors of n that are not multiples of 3.

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

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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]])~))}; \\ FromA019565

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. alsoA293226,A300833.

Sequence in context:A065151 A345874 A338720*A299990 A175193 A353861

Adjacent sequences:A320010 A320011 A320012*A320014 A320015 A320016

KEYWORD

nonn

AUTHOR

Antti Karttunen,Oct 03 2018

STATUS

approved