A365385 -id:A365385 - cp's OEIS frontend

A365386 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A365385(i) = A365385(j) for all i, j >= 1.

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

Offset: 1

Antti Karttunen, Sep 03 2023

Restricted growth sequence transform of the ordered pair [A331410(n), A365385(n)].

For all i, j: A365388(i) = A365388(j) => a(i) = a(j) => A365387(i) = A365387(j).

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

Cf. A003602, A163511, A331410, A365385, A365387, A365388.

Cf. also A334867.

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; };
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
A365385(n) = A331410(A163511(n));
A365386aux(n) = [A331410(n),A365385(n)];
v365386 = rgs_transform(vector(up_to,n,A365386aux(n)));
A365386(n) = v365386[n];

A365388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A334867(i) = A334867(i) and A365386(j) = A365386(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, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25, 13, 26, 7, 27, 14, 28, 4, 29, 15, 30, 8, 31, 16, 32, 1, 33, 17, 34, 9, 35, 18, 36, 5, 37, 19, 38, 10, 39, 20, 40, 3, 41, 21, 42, 11, 43, 22, 44, 6, 45, 23, 46, 12, 47, 24, 48, 2, 49, 25, 41

Offset: 1

Antti Karttunen, Sep 07 2023

nonn

Restricted growth sequence transform of the ordered pair [A334867(n), A365386(n)], or equally, of the quadruplet [A329697(n), A334204(n), A331410(n), A365385(n)].
For all i, j:
  A003602(i) = A003602(j) => a(i) = a(j),
  a(i) = a(j) => A334867(i) = A334867(j),
  a(i) = a(j) => A335880(i) = A335880(j),
  a(i) = a(j) => A365386(i) = A365386(j).

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

Cf. A163511, A329697, A331410, A334204, A334867, A335880, A365385, A365386.

Differs from A003602 and A351090 for the first time at n=99, where a(99) = 41, while A003602(99) = A351090(99) = 50.

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; };
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A334204(n) = A329697(A163511(n));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
A365385(n) = A331410(A163511(n));
A365388aux(n) = [A329697(n),A334204(n),A331410(n),A365385(n)];
v365388 = rgs_transform(vector(up_to,n,A365388aux(n)));
A365388(n) = v365388[n];

A365395 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A365427(i) = A365427(j) for all i, j >= 0.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Sep 04 2023

nonn

Restricted growth sequence transform of the ordered pair [A365425(n), A365427(n)].
Restricted growth sequence transform of the function f(n) = A336390(A163511(n)).
For all i, j: a(i) = a(j) => A365385(i) = A365385(j).

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A000265, A003602, A046523, A163511, A336390, A365385, A365425, A365427, A365394.

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
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A365425(n) = A046523(A000265(A163511(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])); };
A365427(n) = A336467(A163511(n));
A365395aux(n) = [A365425(n), A365427(n)];
v365395 = rgs_transform(vector(1+up_to,n,A365395aux(n-1)));
A365395(n) = v365395[1+n];

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

A366788 a(n) = A366388(A163511(n)).

Original entry on oeis.org

0, 0, 0, 1, 0, 2, 1, 2, 0, 3, 2, 4, 1, 3, 2, 1, 0, 4, 3, 6, 2, 5, 4, 2, 1, 4, 3, 3, 2, 2, 1, 3, 0, 5, 4, 8, 3, 7, 6, 3, 2, 6, 5, 4, 4, 3, 2, 6, 1, 5, 4, 5, 3, 4, 3, 4, 2, 3, 2, 5, 1, 4, 3, 2, 0, 6, 5, 10, 4, 9, 8, 4, 3, 8, 7, 5, 6, 4, 3, 9, 2, 7, 6, 6, 5, 5, 4, 7, 4, 4, 3, 8, 2, 7, 6, 4, 1, 6, 5, 7, 4, 6, 5, 5, 3, 5

Offset: 0

Antti Karttunen, Oct 23 2023

nonn

Cf. A163511, A366388, A366791.

Cf. also A334204, A365385.

A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A366388(n) = if(n<=2, 0, if(isprime(n), 1+A366388(primepi(n)), my(f=factor(n)); (apply(A366388, f[, 1])~ * f[, 2])));
A366788(n) = A366388(A163511(n));

A365387 a(n) = A331410(n) * A331410(A163511(n)).

Original entry on oeis.org

0, 0, 1, 0, 4, 1, 2, 0, 6, 4, 8, 1, 6, 2, 3, 0, 12, 6, 18, 4, 10, 8, 4, 1, 16, 6, 9, 2, 8, 3, 2, 0, 15, 12, 24, 6, 28, 18, 9, 4, 18, 10, 12, 8, 12, 4, 8, 1, 10, 16, 20, 6, 16, 9, 12, 2, 12, 8, 16, 3, 6, 2, 6, 0, 24, 15, 40, 12, 27, 24, 12, 6, 40, 28, 25, 18, 12, 9, 18, 4, 28, 18, 18, 10, 25, 12, 25, 8, 20, 12, 18, 4

Offset: 1

Antti Karttunen, Sep 03 2023

nonn

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

Cf. A163511, A331410, A365385.

Cf. also A334873.

A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
A365387(n) = (A331410(n)*A331410(A163511(n)));

a(n) = A331410(n) * A365385(n).

cp's OEIS Frontend

A365386 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A365385(i) = A365385(j) for all i, j >= 1.

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A365388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A334867(i) = A334867(i) and A365386(j) = A365386(j) for all i, j >= 1.

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A365395 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A365427(i) = A365427(j) for all i, j >= 0.

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A366788 a(n) = A366388(A163511(n)).

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A365387 a(n) = A331410(n) * A331410(A163511(n)).

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