A320014 -id:A320014 - cp's OEIS frontend

A320011 Filter sequence combined from those proper divisors d of n for which +1 == d (mod 3); Restricted growth sequence transform of A319991.

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

Offset: 1

Antti Karttunen, Oct 03 2018

nonn

For all i, j:
  a(i) = a(j) => A320001(i) = A320001(j),
  a(i) = a(j) => A293897(i) = A293897(j).

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

Cf. A293223, A319991, A320010, A320012, A320013, A320014.

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((dA019565(d))); m; };
v320011 = rgs_transform(vector(up_to,n,A319991(n)));
A320011(n) = v320011[n];

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

Original entry on oeis.org

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

Antti Karttunen, Oct 03 2018

nonn

For all i, j:
  a(i) = a(j) => A320005(i) = A320005(j),
  a(i) = a(j) => A293898(i) = A293898(j).

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

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

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((dA019565(d))); m; };
v320012 = rgs_transform(vector(up_to,n,A319992(n)));
A320012(n) = v320012[n];

A320010 Filter sequence combined from those proper divisors of n that are multiples of 3; Restricted growth sequence transform of A319990.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Oct 03 2018

nonn

For all i, j: a(i) = a(j) => A320003(i) = A320003(j).

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

Cf. A319990, A320011, A320012, A320014.

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
A319990(n) = { my(m=1); fordiv(n,d,if((dA019565(d))); m; };
v320010 = rgs_transform(vector(up_to,n,A319990(n)));
A320010(n) = v320010[n];

A320013 Filter sequence constructed from the binary expansions of those proper divisors of n that are not multiples of 3.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Oct 03 2018

nonn

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

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

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

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

Cf. also A293226, A300833.

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((dA019565(d))); m; };
A319992(n) = { my(m=1); fordiv(n,d,if((dA019565(d))); m; };
v320013 = rgs_transform(vector(up_to,n,[A319991(n),A319992(n)]));
A320013(n) = v320013[n];

cp's OEIS Frontend

A320011 Filter sequence combined from those proper divisors d of n for which +1 == d (mod 3); Restricted growth sequence transform of A319991.

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

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A320010 Filter sequence combined from those proper divisors of n that are multiples of 3; Restricted growth sequence transform of A319990.

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A320013 Filter sequence constructed from the binary expansions of those proper divisors of n that are not multiples of 3.

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PARI