A373268 -id:A373268 - cp's OEIS frontend

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.

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

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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