A365425 -id:A365425 - cp's OEIS frontend

A365392 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = [A336158(n), A364255(n), A365425(n)].

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

Offset: 1

Antti Karttunen, Sep 04 2023

Restricted growth sequence transform of triplet [A336158(n), A364255(n), A365425(n)].
For all i, j >= 1:
  a(i) = a(j) => A286531(i) = A286531(j),
  a(i) = a(j) => A305891(i) = A305891(j),
  a(i) = a(j) => A365391(i) = A365391(j),
  a(i) = a(j) => A365421(i) = A365421(j).

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

Cf. A000265, A046523, A163511, A286531, A305891, A336158, A364255, A365425, A365391, A365421.

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));
A364255(n) = gcd(n, A163511(n));
A365392aux(n) = [A364255(n), A046523(A000265(n)), A046523(A000265(A163511(n)))];
v365392 = rgs_transform(vector(up_to,n,A365392aux(n)));
A365392(n) = v365392[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)).

A366792 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A366787(i) = A366787(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, 13, 1, 14, 8, 15, 5, 16, 9, 5, 3, 17, 10, 11, 6, 18, 3, 19, 2, 20, 11, 10, 7, 21, 7, 22, 4, 18, 12, 23, 2, 22, 13, 4, 1, 24, 14, 25, 8, 26, 15, 8, 5, 27, 16, 20, 9, 28, 5, 29, 3, 30, 17, 17, 10, 31, 11, 32, 6, 33, 18, 34, 3

Offset: 0

Antti Karttunen, Oct 23 2023

Restricted growth sequence transform of the ordered pair [A365425(n), A366787(n)].
Restricted growth sequence transform of the function f(n) = A366790(A163511(n)).
For all i, j >= 0: a(i) = a(j) => A366788(i) = A366788(j).

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

Cf. A000265, A163511, A365425, A366787.

Cf. also A365394, A365395.

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)));
A366789(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(primepi(f[k, 1]))^f[k, 2]); };
A366787(n) = A366789(A163511(n));
A366792aux(n) = [A365425(n), A366787(n)];
v366792 = rgs_transform(vector(1+up_to,n,A366792aux(n-1)));
A366792(n) = v366792[1+n];

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

A365394 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A365426(i) = A365426(j) for all i, j >= 0.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Sep 04 2023

Restricted growth sequence transform of the ordered pair [A365425(n), A365426(n)].
Restricted growth sequence transform of the function f(n) = A336470(A163511(n)).
For all i, j: a(i) = a(j) => A334204(i) = A334204(j).

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

Cf. A000265, A003602, A046523, A163511, A336470, A365425, A365426.

Cf. also A350067, A365395, A366792 (compare the scatter plots).

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)));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
A365426(n) = A336466(A163511(n));
A365394aux(n) = [A365425(n), A365426(n)];
v365394 = rgs_transform(vector(1+up_to,n,A365394aux(n-1)));
A365394(n) = v365394[1+n];

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

A366891 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j), A206787(A163511(i)) = A206787(A163511(j)) and A336651(A163511(n)) = A336651(A163511(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, 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, 14, 16, 31, 1, 32, 17, 33, 9, 34, 18, 35, 5, 36, 19, 37, 10, 38, 20, 39, 3, 40, 21, 41, 11, 42, 22, 43, 6, 44, 23

Offset: 0

Antti Karttunen, Nov 04 2023

nonn

Restricted growth sequence transform of the triplet [A365425(n), A206787(A163511(n)), A336651(A163511(n))], and also by conjecture, of sequence b(n) = A351040(A163511(n)).
For all i, j >= 0:
  a(i) = a(j) => A365395(i) = A365395(j),
  a(i) = a(j) => A366874(i) = A366874(j),
  a(i) = a(j) => A366881(i) = A366881(j).

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

Cf. A000265, A000593, A163511, A347385, A351040, A351461, A365425.
Differs from A366806 for the first time at n=105, where a(105) = 52, while A366806(105) = 19.
Differs from A366881 for the first time at n=511, where a(511) = 249, while A366881(511) = 7.

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)));
A206787(n) = sumdiv(n, d, d*issquarefree(2*d));
A336651(n) = { my(f=factor(n>>valuation(n,2))); prod(i=1, #f~, f[i,1]^(f[i,2]-1)); };
A366891aux(n) = [A365425(n), A206787(A163511(n)), A336651(A163511(n))];
v366891 = rgs_transform(vector(1+up_to,n,A366891aux(n-1)));
A366891(n) = v366891[1+n];

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

A365391 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336158(i) = A336158(j) and A365425(i) = A365425(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, 5, 6, 2, 1, 12, 7, 13, 4, 14, 8, 15, 3, 16, 9, 17, 3, 18, 3, 3, 2, 19, 10, 9, 5, 20, 11, 21, 2, 9, 5, 5, 6, 5, 2, 22, 1, 23, 12, 24, 7, 25, 13, 7, 4, 26, 14, 27, 8, 28, 15, 8, 3, 29, 16, 16, 9, 30, 17, 9, 3, 16, 18, 9, 3, 9, 3, 31, 2

Offset: 1

Antti Karttunen, Sep 03 2023

Restricted growth sequence transform of the ordered pair [A336158(n), A365425(n)].
For all i, j:
  A003602(i) = A003602(j) => a(i) = a(j),
  A365392(i) = A365392(j) => a(i) = a(j).

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

Cf. A000265, A003602, A046523, A163511, A336158, A365425, A365392.

Cf. also A286531, 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; };
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));
A365391aux(n) = [A046523(A000265(n)), A046523(A000265(A163511(n)))];
v365391 = rgs_transform(vector(up_to,n,A365391aux(n)));
A365391(n) = v365391[n];

cp's OEIS Frontend

A365392 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = [A336158(n), A364255(n), A365425(n)].

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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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A366792 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A366787(i) = A366787(j) for all i, j >= 0.

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A365394 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A365426(i) = A365426(j) for all i, j >= 0.

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A366891 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j), A206787(A163511(i)) = A206787(A163511(j)) and A336651(A163511(n)) = A336651(A163511(j)) for all i, j >= 0.

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A365391 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336158(i) = A336158(j) and A365425(i) = A365425(j) for all i, j >= 1.

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