A372572 -id:A372572 - cp's OEIS frontend

A372569 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j), A009195(i) = A009195(j) and A009223(i) = A009223(j), for all i, j >= 1.

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

Offset: 1

Antti Karttunen, May 25 2024

nonn

Restricted growth sequence transform of the triple [A009194(n), A009195(n), A009223(n)].

For all i, j: A372570(i) = A372570(j) => a(i) = a(j) => A074389(i) = A074389(j).

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

Cf. A009194, A009195, A009223.

Cf. also A372570, A372572.

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; };
Aux372569(n) = [gcd(n, sigma(n)), gcd(n, eulerphi(n)), gcd(eulerphi(n), sigma(n))];
v372569 = rgs_transform(vector(up_to, n, Aux372569(n)));
A372569(n) = v372569[n];

A372570 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A009194(n), A009195(n), A009223(n), A322361(n), A342671(n)], for all i, j >= 1.

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

Offset: 1

Antti Karttunen, May 25 2024

nonn

Restricted growth sequence transform of the quintuple [A009194(n), A009195(n), A009223(n), A322361(n), A342671(n)].
For all i, j:
  A305801(i) = A305801(j) => a(i) = a(j),
  a(i) = a(j) => A372569(i) = A372569(j),
  a(i) = a(j) => A372572(i) = A372572(j).

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

Cf. A009194, A009195, A009223, A322361, A342671.

Cf. also A305801, A372569, A372572.

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; };
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
Aux372570(n) = [gcd(n, sigma(n)), gcd(n, eulerphi(n)), gcd(eulerphi(n), sigma(n)), gcd(n, A003961(n)), gcd(sigma(n), A003961(n))];
v372570 = rgs_transform(vector(up_to, n, Aux372570(n)));
A372570(n) = v372570[n];

cp's OEIS Frontend

A372569 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j), A009195(i) = A009195(j) and A009223(i) = A009223(j), for all i, j >= 1.

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