A336394 -id:A336394 - cp's OEIS frontend

A336473 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A329697(i) = A329697(j), for all i, j >= 1.

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

Offset: 1

Antti Karttunen, Jul 24 2020

Restricted growth sequence transform of the ordered pair [A278222(n), A329697(n)].

For all i, j: A336460(i) = A336460(j) => a(i) = a(j).

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

Cf. A278222, A329697.

Cf. also A286622, A336394, A336460, A336470, A336471, A336472, A336474.

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; };
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));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
Aux336473(n) = [A278222(n), A329697(n)];
v336473 = rgs_transform(vector(up_to, n, Aux336473(n)));
A336473(n) = v336473[n];

A347374 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A000593(i) = A000593(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, 22, 43, 12

Offset: 1

Antti Karttunen, Aug 29 2021

nonn

Restricted growth sequence transform of the ordered pair [A000593(n), A331410(n)].

For all i, j: A003602(i) = A003602(j) => a(i) = a(j) => A347249(i) = A347249(j).

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

Cf. A000593, A003602, A331410, A347249.

Cf. also A335880, A336390, A336391, A336394 for similar constructions.

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; };
A000593(n) = sigma(n>>valuation(n, 2));
A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
Aux347374(n) = [A331410(n), A000593(n)];
v347374 = rgs_transform(vector(up_to, n, Aux347374(n)));
A347374(n) = v347374[n];

A336392 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336467(i) = A336467(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, 3, 9, 6, 5, 17, 10, 18, 3, 19, 11, 20, 6, 21, 12, 22, 2, 23, 13, 24, 7, 25, 14, 26, 4, 27, 15, 28, 8, 29, 16, 30, 1, 31, 3, 32, 9, 33, 6, 34, 5, 35, 17, 36, 10, 21, 18, 37, 3, 11, 19, 38, 11, 39, 20, 40, 6, 41, 21, 42, 12, 43, 22, 44, 2, 45, 23, 46, 13

Offset: 1

Antti Karttunen, Aug 10 2020

nonn

Restricted growth sequence transform of the ordered pair [A278222(n), A336467(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. A003602, A278222, A324400, A336390, A336391, A336394, A336467.

Cf. also A286622, A336472.

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; };
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));
A000265(n) = (n>>valuation(n,2));
A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
Aux336392(n) = [A278222(n), A336467(n)];
v336392 = rgs_transform(vector(up_to, n, Aux336392(n)));
A336392(n) = v336392[n];

cp's OEIS Frontend

A336473 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A329697(i) = A329697(j), for all i, j >= 1.

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A347374 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A000593(i) = A000593(j), for all i, j >= 1.

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A336392 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336467(i) = A336467(j), for all i, j >= 1.

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