A373379 -id:A373379 - cp's OEIS frontend

A373380 Lexicographically earliest infinite sequence such that a(i) = a(j) => A373145(i) = A373145(j), A373362(i) = A373362(j), and A373364(i) = A373364(j), for all i, j >= 1.

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

Offset: 1

Antti Karttunen, Jun 03 2024

nonn

Restricted growth sequence transform of the triple [A373145(n), A373362(n), A373364(n)], i.e., the triple [gcd(x, y), gcd(x, z), gcd(y, z)], where x=A001414(n), y=A003415(n), z=A276085(n).
For all i, j >= 1:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A373367(i) = A373367(j).

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

Cf. A001414, A003415, A276085, A305800, A373145, A373362, A373364, A373367.

Cf. also A373150, A373379.

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; };
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
Aux373380(n) = { my(x=A001414(n), y=A003415(n), z=A276085(n)); [gcd(x, y), gcd(x, z), gcd(y, z)]; };
v373380 = rgs_transform(vector(up_to, n, Aux373380(n)));
A373380(n) = v373380[n];

A373981 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A107463(n), A181819(n), A373247(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, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 24, 25, 26, 27, 3, 28, 29, 30, 3, 31, 3, 32, 33, 34, 3, 35, 36, 37, 38, 39, 3, 40, 29, 41, 42, 43, 3, 44, 3, 45, 46, 47, 48, 49, 3, 50, 51, 52, 3, 53, 3, 54, 46, 55, 48, 56, 3, 57, 58, 59, 3, 60, 42, 61, 62, 63, 3, 64, 38, 65, 66, 67, 68, 69, 3, 70, 71

Offset: 1

Antti Karttunen, Jun 24 2024

nonn

Restricted growth sequence transform of the triple [A107463(n), A181819(n), A373247(n)].
For all i, j >= 1:
  A305801(i) = A305801(j) => a(i) = a(j),
  a(i) = a(j) => A373250(i) = A373250(j) => A101296(i) = A101296(j),
  a(i) = a(j) => A373976(i) = A373976(j).

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

Cf. A107463, A181819, A373247.
Cf. A101296, A305801, A373250, A373976.
Cf. also A373379, A373980.

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; };
A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
A107463(n) = if(n<=1,n,if(isprime(n),1,A001414(n)));
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
Aux373981(n) = { my(s=A181819(n)); [A107463(n), s, n%s]; };
v373981 = rgs_transform(vector(up_to, n, Aux373981(n)));
A373981(n) = v373981[n];

cp's OEIS Frontend

A373380 Lexicographically earliest infinite sequence such that a(i) = a(j) => A373145(i) = A373145(j), A373362(i) = A373362(j), and A373364(i) = A373364(j), for all i, j >= 1.

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