A336158 -id:A336158 - cp's OEIS frontend

A336470 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336158(i) = A336158(j), for all i, j >= 1.

1, 1, 2, 1, 2, 2, 3, 1, 4, 2, 5, 2, 3, 3, 6, 1, 2, 4, 7, 2, 8, 5, 9, 2, 4, 3, 10, 3, 11, 6, 12, 1, 13, 2, 8, 4, 7, 7, 8, 2, 5, 8, 14, 5, 15, 9, 16, 2, 17, 4, 6, 3, 18, 10, 13, 3, 19, 11, 20, 6, 12, 12, 21, 1, 8, 13, 22, 2, 23, 8, 24, 4, 7, 7, 15, 7, 25, 8, 26, 2, 27, 5, 28, 8, 6, 14, 29, 5, 9, 15, 19, 9, 25, 16, 19, 2, 3, 17, 30, 4, 31, 6, 32, 3, 33

Offset: 1

Antti Karttunen, Jul 24 2020

nonn

Restricted growth sequence transform of the ordered pair [A336466(n), A336158(n)].
For all i, j:
  A336460(i) = A336460(j) => a(i) = a(j),
  a(i) = a(j) => A329697(i) = A329697(j),
  a(i) = a(j) => A336471(i) = A336471(j).

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

Cf. A336158, A336466.

Cf. also A329697, A336160, A336471.

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; };
A000265(n) = (n>>valuation(n,2));
A336466(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1))^f[k,2])); };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
Aux336470(n) = [A336466(n), A336158(n)];
v336470 = rgs_transform(vector(up_to, n, Aux336470(n)));
A336470(n) = v336470[n];

A336390 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 5, 2, 6, 1, 7, 4, 8, 3, 9, 3, 3, 2, 10, 5, 11, 2, 12, 6, 2, 1, 6, 7, 6, 4, 13, 8, 14, 3, 15, 9, 16, 3, 17, 3, 3, 2, 4, 10, 18, 5, 19, 11, 18, 2, 20, 12, 12, 6, 21, 2, 22, 1, 23, 6, 24, 7, 6, 6, 7, 4, 25, 13, 26, 8, 6, 14, 8, 3, 27, 15, 15, 9, 28, 16, 29, 3, 30, 17, 14, 3, 9, 3, 29, 2, 31, 4, 17, 10, 32, 18, 33, 5, 34

Offset: 1

Antti Karttunen, Aug 10 2020

nonn

Restricted growth sequence transform of the ordered pair [A336467(n), A336158(n)].
For all i, j:
  A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),
  a(i) = a(j) => A331410(i) = A331410(j),
  a(i) = a(j) => A336391(i) = A336391(j).

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

Cf. A003602, A324400, A336158, A336467, A336391, A336393.

Cf. also A336470.

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
Aux336390(n) = [A336158(n), A336467(n)];
v336390 = rgs_transform(vector(up_to, n, Aux336390(n)));
A336390(n) = v336390[n];

A336159 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 6, 4, 7, 1, 3, 5, 6, 3, 8, 6, 9, 2, 10, 6, 11, 4, 9, 7, 12, 1, 13, 3, 14, 5, 15, 6, 16, 3, 15, 8, 17, 6, 18, 9, 19, 2, 10, 10, 20, 6, 17, 11, 21, 4, 16, 9, 22, 7, 19, 12, 23, 1, 13, 13, 6, 3, 8, 14, 9, 5, 15, 15, 18, 6, 24, 16, 19, 3, 25, 15, 17, 8, 26, 17, 27, 6, 17, 18, 28, 9, 27, 19, 29, 2, 6, 10, 30, 10, 17, 20, 22, 6, 31

Offset: 1

Antti Karttunen, Jul 11 2020

Restricted growth sequence transform of the ordered pair [A278222(n), A336158(n)], i.e., of the ordered pair [A046523(A005940(1+n)), A046523(A000265(n))].

For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

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

Cf. A000265, A005940, A046523, A278222, A336158.

Cf. also A003602, A286163, A286622, A291762, A324400, A336149, A336156, A336157, A336160, A336162.

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; };
A000265(n) = (n>>valuation(n,2));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
A336158(n) = A046523(A000265(n));
Aux336159(n) = [A278222(n), A336158(n)];
v336159 = rgs_transform(vector(up_to, n, Aux336159(n)));
A336159(n) = v336159[n];

A336471 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 1, 4, 2, 3, 2, 3, 3, 5, 1, 2, 4, 6, 2, 7, 3, 6, 2, 4, 3, 8, 3, 6, 5, 6, 1, 7, 2, 7, 4, 6, 6, 7, 2, 3, 7, 9, 3, 10, 6, 9, 2, 11, 4, 5, 3, 6, 8, 7, 3, 12, 6, 9, 5, 6, 6, 13, 1, 7, 7, 9, 2, 12, 7, 9, 4, 6, 6, 10, 6, 12, 7, 9, 2, 14, 3, 6, 7, 5, 9, 12, 3, 6, 10, 12, 6, 12, 9, 12, 2, 3, 11, 13, 4, 6, 5, 6, 3, 15

Offset: 1

Antti Karttunen, Jul 22 2020

nonn

Restricted growth sequence transform of the ordered pair [A329697(n), A336158(n)].
For all i, j:
  A336470(i) = A336470(j) => a(i) = a(j)
  a(i) = a(j) => A336396(i) = A336396(j),
  a(i) = a(j) => A336469(i) = A336469(j) => A336477(i) = A336477(j).
This sequence has an ability to see where the terms of A003401 are, as they are the indices of zeros in A336469. Specifically, they are numbers k that satisfy the condition A329697(k) = A001221(A336158(k)), i.e., numbers for which A329697(k) is equal to the number of distinct prime divisors of the odd part of k. See also comments in array A334100.

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

Cf. A000265, A003401, A046523, A329697, A334100, A336158.

Cf. also A003602, A324400, A336159, A336160, A336396, A336469, A336470, A336472, A336473, A336477.

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
Aux336471(n) = [A329697(n), A336158(n)];
v336471 = rgs_transform(vector(up_to, n, Aux336471(n)));
A336471(n) = v336471[n];

A336156 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jul 11 2020

nonn

Restricted growth sequence transform of the ordered pair [A007814(1+n), A336158(n)]. Note that A007814(1+n) gives the number of trailing 1-bits in the binary expansion of n.

For all i, j: A324400(i) = A324400(j) => a(i) = a(j).

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

Cf. A000265, A007814, A046523, A336158.

Cf. also A324400, A336152, A336153, A336154, A336155.

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A007814(n) = valuation(n,2);
Aux336156(n) = [A007814(1+n), A336158(n)];
v336156 = rgs_transform(vector(up_to, n, Aux336156(n)));
A336156(n) = v336156[n];

A336160 Lexicographically earliest infinite sequence such that a(i) = a(j) => A335915(i) = A335915(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 6, 3, 7, 1, 8, 4, 9, 3, 7, 5, 10, 2, 11, 6, 12, 3, 13, 7, 5, 1, 14, 8, 15, 4, 16, 9, 17, 3, 13, 7, 18, 5, 19, 10, 20, 2, 11, 11, 15, 6, 21, 12, 22, 3, 22, 13, 23, 7, 24, 5, 19, 1, 25, 14, 26, 8, 27, 15, 28, 4, 29, 16, 30, 9, 22, 17, 31, 3, 32, 13, 33, 7, 34, 18, 35, 5, 36, 19, 25, 10, 14, 20, 37, 2, 38, 11, 39, 11, 40, 15, 41, 6, 42

Offset: 1

Antti Karttunen, Jul 11 2020

nonn

Restricted growth sequence transform of the ordered pair [A335915(n), A336158(n)].

For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A336161(i) = A336161(j).

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

Cf. A000265, A046523, A324400, A335915, A336158, A336159, A336161, A336162.

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A335915(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1)*A000265(f[k,1]+1))^f[k,2])); };
Aux336160(n) = [A335915(n), A336158(n)];
v336160 = rgs_transform(vector(up_to, n, Aux336160(n)));
A336160(n) = v336160[n];

A336391 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 5, 1, 6, 4, 6, 3, 7, 3, 3, 2, 8, 3, 9, 2, 10, 5, 2, 1, 5, 6, 5, 4, 10, 6, 5, 3, 6, 7, 6, 3, 11, 3, 3, 2, 4, 8, 12, 3, 10, 9, 12, 2, 12, 10, 10, 5, 3, 2, 13, 1, 12, 5, 10, 6, 5, 5, 6, 4, 14, 10, 15, 6, 5, 5, 6, 3, 16, 6, 6, 7, 17, 6, 17, 3, 14, 11, 5, 3, 7, 3, 17, 2, 6, 4, 11, 8, 14, 12, 6, 3, 18

Offset: 1

Antti Karttunen, Aug 10 2020

nonn

Restricted growth sequence transform of the ordered pair [A331410(n), A336158(n)].
For all i, j:
  A336390(i) = A336390(j) => a(i) = a(j)
  a(i) = a(j) => A336921(i) = A336921(j),
  a(i) = a(j) => A336922(i) = A336922(j) => A336923(i) = A336923(j).

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

Cf. A331410, A336467, A336390, A336921, A336922, A336923.

Cf. also A336471.

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
Aux336391(n) = [A331410(n), A336158(n)];
v336391 = rgs_transform(vector(up_to, n, Aux336391(n)));
A336391(n) = v336391[n];

A336460 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A336158(n), A336466(n)], for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 3, 5, 9, 3, 10, 6, 11, 2, 12, 7, 13, 4, 14, 8, 15, 1, 16, 3, 17, 5, 18, 9, 19, 3, 20, 10, 21, 6, 22, 11, 23, 2, 24, 12, 25, 7, 26, 13, 27, 4, 28, 14, 29, 8, 30, 15, 31, 1, 32, 16, 33, 3, 34, 17, 35, 5, 18, 18, 22, 9, 36, 19, 37, 3, 38, 20, 39, 10, 40, 21, 41, 6, 42, 22, 43, 11, 44, 23, 45, 2, 7, 24, 46, 12, 47, 25, 48, 7, 49

Offset: 1

Antti Karttunen, Jul 24 2020

nonn

Restricted growth sequence transform of the ordered triple [A278222(n), A336158(n), A336466(n)].
For all i, j:
  A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),
  a(i) = a(j) => A336159(i) = A336159(j),
  a(i) = a(j) => A336470(i) = A336470(j) => A336471(i) = A336471(j),
  a(i) = a(j) => A336472(i) = A336472(j),
  a(i) = a(j) => A336473(i) = A336473(j).

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

Cf. A278222, A336158, A336466.

Cf. A003602, A324400, A336159, A336470, A336471, A336472, A336473.

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; };
A000265(n) = (n>>valuation(n,2));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
A336158(n) = A046523(A000265(n));
A336466(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1))^f[k,2])); };
Aux336460(n) = [A278222(n), A336158(n), A336466(n)];
v336460 = rgs_transform(vector(up_to, n, Aux336460(n)));
A336460(n) = v336460[n];

A351040 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336158(i) = A336158(j), A206787(i) = A206787(j) and A336651(i) = A336651(j) for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 17, 5, 18, 10, 19, 3, 20, 11, 21, 6, 22, 12, 23, 2, 24, 13, 25, 7, 26, 14, 25, 4, 27, 15, 28, 8, 29, 16, 30, 1, 31, 17, 32, 9, 33, 17, 34, 5, 35, 18, 36, 10, 33, 19, 37, 3, 38, 20, 39, 11, 40, 21, 41, 6, 42

Offset: 1

Antti Karttunen, Jan 31 2022

Restricted growth sequence transform of the ordered triplet [A336158(n), A206787(n), A336651(n)].
For all i, j >= 1:
  A003602(i) = A003602(j) => a(i) = a(j),
  a(i) = a(j) => A336390(i) = A336390(j) => A336391(i) = A336391(j),
  a(i) = a(j) => A347374(i) = A347374(j),
  a(i) = a(j) => A351036(i) = A351036(j) => A113415(i) = A113415(j),
  a(i) = a(j) => A351461(i) = A351461(j).
From Antti Karttunen, Nov 23 2023: (Start)
Conjectured to be equal to the lexicographically earliest infinite sequence such that b(i) = b(j) => A000593(i) = A000593(j), A336158(i) = A336158(j) and A336467(i) = A336467(j), for all i, j >= 1 (this was the original definition). In any case it holds that a(i) = a(j) => b(i) = b(j) for all i, j >= 1. See comment in A351461.
(End)

Antti Karttunen, Table of n, a(n) for n = 1..65539

Cf. A000265, A000593, A336158, A336467.
Cf. also A003602, A336390, A336391, A351037, A366891.
Differs from A347374 for the first time at n=103, where a(103) = 48, while A347374(103) = 30.
Differs from A351035 for the first time at n=175, where a(175) = 80, while A351035(175) = 78.
Differs from A351036 for the first time at n=637, where a(637) = 272, while A351036(637) = 261.

up_to = 65539;
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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
A336158(n) = A046523(A000265(n));
A206787(n) = sumdiv(n, d, d*(d % 2)*issquarefree(d));
A336651(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i,1],1,f[i,1]^(f[i,2]-1))); };
Aux351040(n) = [A336158(n), A206787(n), A336651(n)];
v351040 = rgs_transform(vector(up_to, n, Aux351040(n)));
A351040(n) = v351040[n];

Original definition moved to the comment section and replaced with a definition that is at least as encompassing, and conjectured to be equal to the original one. - Antti Karttunen, Nov 23 2023

A336148 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 5, 10, 11, 12, 2, 13, 14, 15, 8, 16, 17, 18, 5, 19, 20, 21, 11, 22, 23, 24, 2, 25, 26, 27, 14, 28, 29, 30, 8, 31, 32, 33, 17, 34, 35, 36, 5, 37, 38, 39, 20, 40, 41, 25, 11, 42, 43, 44, 23, 45, 46, 47, 2, 48, 49, 50, 26, 51, 32, 52, 14, 53, 54, 34, 29, 55, 56, 57, 8, 58, 59, 60, 32, 61, 62, 63, 17, 64, 65, 30, 35, 66, 67, 68, 5, 69, 70, 71, 38, 72, 73, 74, 20, 75

Offset: 1

Antti Karttunen, Jul 12 2020

nonn

Restricted growth sequence transform of the ordered pair [A278221(n), A336158(n)], i.e., of the ordered pair [A046523(A122111(n)), A046523(A000265(n))].

For all i, j: A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j).

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

Cf. A000265, A046523, A064989, A122111, A278221, A336158.

Cf. also A286621, A318890, A324400, A336146, A336149, A336159.

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; };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
A000265(n) = (n>>valuation(n,2));
A336158(n) = A046523(A000265(n));
Aux336148(n) = [A278221(n),A336158(n)];
v336148 = rgs_transform(vector(up_to, n, Aux336148(n)));
A336148(n) = v336148[n];

cp's OEIS Frontend

A336470 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336466(i) = A336466(j) and A336158(i) = A336158(j), for all i, j >= 1.

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A336390 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A336158(i) = A336158(j), for all i, j >= 1.

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A336159 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336158(i) = A336158(j), for all i, j >= 1.

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A336471 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A336158(i) = A336158(j), for all i, j >= 1.

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A336156 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A336158(i) = A336158(j), for all i, j >= 1.

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A336160 Lexicographically earliest infinite sequence such that a(i) = a(j) => A335915(i) = A335915(j) and A336158(i) = A336158(j), for all i, j >= 1.

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A336391 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A336158(i) = A336158(j), for all i, j >= 1.

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A336460 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A336158(n), A336466(n)], for all i, j >= 1.

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A351040 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336158(i) = A336158(j), A206787(i) = A206787(j) and A336651(i) = A336651(j) for all i, j >= 1.

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