A353521 -id:A353521 - cp's OEIS frontend

A344025 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A003557(i) = A003557(j), for all i, j >= 1.

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

Offset: 1

Antti Karttunen, May 07 2021

nonn

Restricted growth sequence transform of the ordered pair [A003415(n), A003557(n)], where A003415(n) is the arithmetic derivative of n, and A003557(n) is n divided by its largest squarefree divisor.
For all i, j:
  parent(i) = parent(j) => a(i) = a(j),
  a(i) = a(j) => A342001(i) = A342001(j),
  a(i) = a(j) => A369051(i) = A369051(j) => A085731(i) = A085731(j).
Where "parent" can be any of the sequences A351236, A351260, A353520, A353521, A369050, for example.

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

Cf. A003415, A003557, A085731, A342001, A369051.

Cf. also A305800, A351236, A351260, A353520, A353521, A369050, and also A353523.

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
Aux344025(n) = [A003415(n), A003557(n)];
v344025 = rgs_transform(vector(up_to, n, Aux344025(n)));
A344025(n) = v344025[n];

A353522 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A003415(i) = A003415(j), for all i, j >= 1, where A000035 and A003415 compute the parity and the arithmetic derivative of their argument.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Apr 27 2022

nonn

Restricted growth sequence transform of the ordered pair [A000035(n), A003415(n)].
For all i, j:
   A353520(i) = A353520(j) => A353521(i) = A353521(j) => a(i) = a(j).

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

Cf. A000035, A003415.

Cf. also A305801, A353520, A353521.

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; };
A000035(n) = (n%2);
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
Aux353522(n) = [A000035(n), A003415(n)];
v353522 = rgs_transform(vector(up_to,n,Aux353522(n)));
A353522(n) = v353522[n];

A374040 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003415(n), A085731(n), A007814(n), A007949(n)], for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jul 01 2024

nonn

Restricted growth sequence transform of the quadruple [A003415(n), A085731(n), A007814(n), A007949(n)].
For all i, j >= 1:
  A305900(i) = A305900(j) => a(i) = a(j),
  a(i) = a(j) => A322026(i) = A322026(j),
  a(i) = a(j) => A369051(i) = A369051(j) => A083345(i) = A083345(j),
  a(i) = a(j) => b(i) = b(j), where b can be any of the sequences listed at the crossrefs-section, under "some of the other matched sequences".

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A003415, A007814, A007949, A085731.
Some of the other matched sequences (see comments): A083345, A359430, A369001, A369004, A369643, A369658, A373143, A373474, A373483.
Cf. also A322026, A353521, A369051, A373268, A372573, A374131 for similar and related constructions.
Differs from A305900 first at n=77, where a(77) = 50, while A305900(77) = 59.

up_to = 100000;
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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
Aux374040(n) = { my(d=A003415(n)); [d, gcd(n,d), valuation(n,2), valuation(n,3)]; };
v374040 = rgs_transform(vector(up_to, n, Aux374040(n)));
A374040(n) = v374040[n];

cp's OEIS Frontend

A344025 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A003557(i) = A003557(j), for all i, j >= 1.

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A353522 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A003415(i) = A003415(j), for all i, j >= 1, where A000035 and A003415 compute the parity and the arithmetic derivative of their argument.

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A374040 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A003415(n), A085731(n), A007814(n), A007949(n)], for all i, j >= 1.

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